









'?&> 









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■ 












THE 



SYSTEM OF CALCULATING 



DIAMETER, CIRCUMFERENCE, AREA, 



AND 



SQUARING THE CIRCLE. 



TOGETHER WITH 



INTEEEST AND MISCELLANEOUS TABLES, AND 
OTHER INFORMATION. 



BY 

JAMES MORTON. 



'x 



n No. . ...o i 



PHILADELPHIA: 
CLAXTON, EEMSEN & HAFFELFINGER, 

024, 626 & 628 Market Street. 
1879. 



% 









Entered, according to Act of Con g r ess , in the year 1 3 

JAMES MORTON, 
in the Office of the librarian of Congress, at Washington. 



y^ -Xj^ ^tv* 

r^tftf* J. FAOAN A BOH, ^fc& V 

~C| , ELF.CTROTYPK.RS, IMIILAH A. *w^^ 



XT- 



— v 5 ^ 



n 



PREFACE. 



It is not the purpose of the writer to introduce 
to the public any new principle, but the result of 
laborious calculations culminating in the final elu- 
cidation of facts. 

The Interest Table is calculated on the usual 
custom adopted by bankers — of 30 days to the 
month. 

The other tables are collated from the best 
authorities. 



in 



CONTENTS. 



PAGE 

tlie clrcle, and ttie measurement of angles . . .9 

Definitions 9 

To Insceibe an Equilateral Tei angle in a Given Circle . 10 
To Inscribe a Square in a Given Circle . . . .11 
To Find tile Approximate Square Roots of Surds or Prime 

Numbers, and tlte Correct Area of their Squares . 15 
TnE Square Described on tlte Diagonal of a Given Square 

is Equivalent to Double the Given Square . . 18 
Two Sides of a Right- Angled Triangle Given to Find the 

Other 19 

A Regular Polygon is One vnicn is both Equilateral and 

Equiangular 21 

The Area of a Circle is Equal to the Product of Half 

the Radius by the Circumference * . . . .22 
Proposition, Theorem, and Calculation of the Limit of 

the Circle 23 

Calculation of Right- Angled Triangle in Polygon 

of 12 Sides ......*.. 25 

Calculation of Right- Angled Triangle in Polygon 

of 24 Sides 28 

Summary of Calculating the Angles of Polygons 

from 12 to 3145728 32 

Area of the Circle by Per Cent. 38 

TnE Square of the Circle 39 

Measurement by Parallel Lines 43 

Table of Polygons 48 

1* v 



VI CONTENTS. 

PAGE 

To Find the Length of an Arc of a Circle containing any 

Number of Degrees 51 

The Earth's Equatopial Radius .... . .51 

The Earth's Equatorial Diameter 51 

The Earth's Circumference at the Equator 

Calculation of the Diameter and Geboumfebbnoe of 
TnE Earth in French Metres .... 

The Earth 53 

Table of the Lengths of Days in Different Latitudes . 54 
Table Showing Difference of Time .... 
Measure or Division or Tin-; Circle .... 
Geographical or Nautical Measure .... 

Gunter's Chain 5G 

Long Measure 

Square Measure 

The Earth's Motion 57 

Calculation of the Distance of the Bun prom the Earth . 50 

Solar Year 59 

The Sun's Heat 60 

Kepler's Discoveries 61 

A Day 

A MoNTn 

A Year G4 

The Stars 66 

Length of Degrees of Longitude in Different Latitudes . 71 

Equation of Payments 71 

Table of Days for Interest, etc 73 

Table of Experiments with Wire and Hempen Rope and 

Chain 

Interest Table 74 

Compound Interest by Decimals 85 

Table of Compound Interest 85 

Cent Table at 6 Per Cent 8G 

Simple Interest • . .88 



CONTENTS. Vll 

PAGE 

Rules for Calculating Interest 88 

Table of $100, Compound Interest, at 6 Per Cent. . . 89 

Discount 90 

Table of Approximate Value of Foreign Coins . .90 

Reduction of Foreign Monet 92 

Insurance 93 

Averages 94 

Fellowship 96 

Weights and Measures 97 

Diamond Weight . . 97 

Articles Sold by Number 97 

Paper Measures 97 

Cloth Measures 97 

Cubic Measures . 97 

Book Measures . 98 

Apothecaries 1 Weights ....... 98 

Troy Weights 98 

Avoirdupois Weights 99 

Cubic or Solid Measures 99 

Scripture Long Measures 99 

Liquid Measures 100 

Dry Measures 100 

The Melting-Point of Metals and Effect on Bodies by 

Heat 101 

Table of the Temperature Required to Ignite Different 

Combustible Substances 102 

Weight of Nails 102 

Weight of Metallic Balls 103 

Rules to Ascertain the Weight of Copper and Lead, and 

of Brass Castings 103, 10-4 

Table Showing Strength of Rope 104 

Table of Specific Gravities 105 

Gravitation 109 

Water 109 



Vlll CONTENTS. 

PA'.F, 

The HEEEPATns' Analysis . . . . . .118 

Wind 113 

Velocity and Peessuee of Wind 114 

Teaction 115 

oompeessibility of llquids hg 

To Measuee Round Timbee HG 

Capacity of Cisteens in U. S. Gallons . . . .117 

Hills in an Acee of Geoino 117 

Alloys 118 

Miscellaneous 118 

compaeative weight of tlmbeb ...... 119 

Table of Boaed Measube 120 

Moese Telegeaph Alphabet 122 

Resistance Measurement of No. ( .» Galvanized Ebon Wibe . 
Table of Numbee of Feet Babe Ooppeb Wibe to the 

Pound L-24 

Weigiit of Insulated Office Wiees 121 

Table of Ieon Wiee L26 

Decimal Table foe Reducing Vulgab to Decimal Fbao- 

tions 127 

IIeat-Radiatinu Poweb op Diffebent Bodies . . . 127 
Table foe Finding the Distance of Objects at Ska in 

Statute Miles 

IIeat-Conductino Poweb of Diffebent Bode . .128 

Peoducts Obtained feom Coal L29 

Sign of Death 

Ieon 131 

PUDDLING-FUENACES FOE IeON 

Impeoved Cupola Fuen ace L8fi 

Ancient Geanite Woeks in the East Indian Empiee . .139 



DIAMETER, CIRCUMFERENCE, AREA, 

AND 

SQUARING THE CIRCLE. 



The Circle, and the Measurement of Angles. 

Definitions. 

A Circle is a plane figure bounded by a curved line, every 
part of which is equidistant from a poiut within called the 
centre, and contains as great an area within the same out- 
line or perimeter as any other form. 

The line, A B, drawn 
through the centre is 
called a diameter. 

The straight line 
drawn from the centre, 
D, to the circumference, 
C, is called a radius or 
semidiameter. 



Any part of a circum- 
ference is called an arc. 
A C being an arc of the 
one-fourth of the circumference. 




Fig. 1. 



The straight line, C B, is called a chord. 
A diameter is greater than any other chord. 



10 



GEOMETRY. 



Every diameter divides the circle and its circumference 
each into two equal parts. 



To Inscribe an Equilateral Triangle in a given Circle. 

To inscribe an equilateral triangle in a circle, divide the 
circle into three equal parts ; draw the chords A C, A B, C B. 

The area of this triangle 
is equal to half the product 
of its base and altitude. 

Let A B C be a triangle, 
and B I) perpendicular to 

the base ; then will its area 
be equal to one-half of 
ACxBD. 

For draw C E parallel 
to A B, and 1>E parallel 
to A C, completing the par- 
allelogram A E. Then the 
triangle, A B C, is half the parallelogram A BCE, which 
has the same base, A C, and the same altitude, B 1) ; but the 

area of the paral- 
E lelogram is equal 
to A C x B D ; 
hence, that of the 
triangle must be 
i A C X B D or 
A C x 5 B D. 

Two trian 
of equal altitude 
are to each other 
as their bases, and 




Fig. 2. 




Fig. 3. 



two triangles of equal bases are to each other as their alti- 



GEOMETRY. 11 

tudes ; and triangles generally are to each other as the prod- 
ucts of their bases and altitudes. 

The square of the one side of an equilateral triangle in- 
scribed in a circle is equal to three-fourths the area of a 
square described without the circle and tangent thereunto. 
Therefore, by squaring the diameter and extracting the 
square root of three-fourths the product, you have the one 
side of an equilateral triangle drawn in a circle. 

Example.— A circle the diameter of two hundred square 
thirds equal to 115.47 + feet and the area of the circum- 
scribed square being thirteen thousand three hundred and 
thirty-three and a third square feet. 

200 
200 
1)40000 



3 



13333| 

6666| 
33331 



10000 = | the area. 

The square root of (10000) ten thousand feet equals one 
hundred feet, the side of the equilateral triangle. 

Or, multiply the diameter by the decimal .86 T %. 

For the area of the triangle, multiply the square of the 
side of the triangle by the decimal .4330. 



To Inscribe a Square in a Given Circle. 

To inscribe a square in a circle, draw two diameters, A B, 
CD, intersecting each other at right angles; join their 
extremities, ACBD. 



12 



SQUARE ROOT. 



A square inscribed inside of a circle is half the size of a 

square described outside 
of a circle. 

For the side of an in- 
scribed square, multiply 
the diameter by the deci- 
mal .70711. 

Let the diameter, A B, 
be 128 feet; then 128 X 

70711 =90fVoV Near 
enough for all practical 
purp 

You cannot extract 
the square root from 128, 

an imperfect power, but you may approximate it. G4 is 
a perfect power and a square number, as 8x8 = G4; but 
when you take a prime number, you must reduce it to a 
fractional number to extract the square root, as 1 reduced 
to 144=12 X 12, the root being 1 \ i 2 i ) two equivalent to 
f#f , the square of which is T V^, and three. 




This square, 4] x4] f'< 1 1, equals 1^ T 1 (7 
square feet, the square root of which 
is seventeen sixteenths, 4.2") x 4.25 = 



1 Q 6 2 5 

lu i owe* 



41x41 = 18^ square feet, 



Fig. 5. 



reduced to sixteenths, equal 17 square 
sixteenths on a side, 17 X 17 = 289. 
289^-16 = 18^. 

Note. — A square number cannot have more 
places of figures than double the places of the root, but .sometimes 
less; for instance 10, the square of which is 100, one less than double 
the places of the root. 

When the number of places in a given sum is an odd number, the 
left hand period will contain one figure, as 1.44; but the root will be 



SQUARE ROOT. 13 

composed of as many figures as there are periods, 12 being the square 
root of 144. 

Explanation of the Process of Extracting the Square Root. — 
First, point off the given number into periods of two figures 
each, by putting a dot between every two figures to the left, 
and also to the right, when there are decimals. 

Secondly, find the greatest square in the left hand period, 
and write its root in the quotient. Subtract the square of 
this root from the left hand period, and to the remainder 
bring down the next period for a dividend. 

Thirdly, double the root already found for a divisor ; as- 
certain how many times the divisor is contained in the divi- 
dend, excepting the right hand figure, and place the result 
in the root, also at the right hand of the divisor and under 
the same, and multiply the divisor by this figure. Subtract 
the product from the dividend, and to the remainder bring 
down the next period for a new dividend, and so continue 
until all the periods are brought down. 

If any dividend shall be too small to contain the divisor, 
place a cipher in the root, also to the right of the divisor, 
and bring down the next period to the right hand of the 
dividend, and proceed in the work. 

Take eighteen square feet and extract the square root by 
decimals, thus : 

18(4.24264 + 
16 



82 


200 






2 


164 






844 


3600 


84846 


543600 


4 


3376 


6 

848524 


509076 


8482. 


22400 


3452400 


2 


16964 


4 


.3394096 


84846 
2 


543600 


848528 


58304 



14 SQUARE ROOT. 

You may proceed iu this manner, ad infinitum, without 
reaching a finality ; but in the following process you may 
always accomplish a final result. 

18 (4f 4f 

16 JJ 

8 2 16 

1 
_1 
18 

This is not 4~ x 4f, because that would make the same 
result as the previous example, but g of 4, and not of the 
fraction; its equivalent being more than four and twenty-four 
hundredths, and less than twenty-five hundredths, about 

A OAJ 7 4 8 8 

^• z %Ty888- 

The square root of 288 by this proa 





288(16 


16ff 




1 


16J| 


26 


188 


96 


6 


156 


16 


32 


32 


16 

16 



This is sixteen times sixteen, and thirty-two thirty-seconds 
of sixteen — twice for the four sides of the square, thirty-two 
representing two sides. That is, the square of sixteen "equals 
two hundred and fifty-six and the remainder; viz., thirty- 
two is proportionately distributed by this process, and, by 
the other process, the square root of the same is as follow- : 

16.97056274847714058562+. 



SQUARE ROOT. 15 

To Find the Approximate Square Roots of Surds or Prime 
Numbers, and the Correct Area of their Squares. 

Take, for example, one hundred feet square, equal to ten 
thousand square feet ; the side of this square being one hundred 
feet, and the half of this square being five thousand square 
feet, and a prime number can only be squared in the follow- 
ing manner : 



140 



50.00 

Reducing the side to fractions of one hundred and forty, 
and squaring the same, then dividing by the square of one 
hundred and forty, you have as follows : 



50.00 ( 70^* 
49 


70 
70 


70 
100 


100 


4900 
50 


140)7000(50 
700 




50 






140 
140 


140 

7010 0. 

' U 140 


5600 
140 


9800 
100 


19600 


9900 
9900 




8910000 
89100 




19600 ) 98010000 ( 5000 
98000 



10000 

This remainder, 10000, is the square of the numerator of 
the fraction |f g, viz., 100 X 100 = 10000 ; the remainder will 
always correspond to the square of the numerator of the frac- 
tion, and the product will always be plus the square of the nu- 
merator. Again, reduce 5000 to square 140 = 98000000, thus : 



16 





SQUAEE ROOT. 




140 


140 


140 


140 


70 


10 


5600 


9800 . 


1400 


140 


9800 


1400 


19600 


7840000 


560000 


5000 


88200 


1400 


98000000 


96040000 
1960000 


1960000 



98000000 

The remainder, or fraction, is X 10, its square root, 
proof of the above calculation, take the square 100. 



As 



. 



140 




140 


140 




100 


5600 




14000 


140 




14(ioo 


19600 




56000000 


10000 




14000 


2)196000000 




196000000 


98000000 






98.00.00.00 ( 9899 ,%\% 9 8 


9899 


81 




9799 


188 1700 


9899 


89091 


8 1504 


9899 


89091 


1969 19600 


89091 


69293 


9 17721 


89091 


89001 


19789 187900 


79192 19" 


"98) 97000301 (4899A 


9 178101 


89091 


79192 


19798 9799 


48991 


178083 




4899A 


158384 




98000000 


196990 
178182 



188081 






SQUARE ROOT. 



17 



In this manner can be calculated the area of the diagonal 
square, and the correct amount be ascertained ; but the 
exact side of the diagonal square is only approximated, the 
side being less than 70|f£, that is, 70 x 70 and jJ$ of 70 
on the two angular sides, and in this manner the square 
root of 2 may be also approximated,. viz. : 

1.414213P"-"* 



1.414213 || 

4242639 
1414213 
2828426 
5656852 
1414213 
5656852 
1414213 

795315| 
795315^ 

2.000000000000 



4 14213 
531 5H 
14213 



1.414213 



A complex fraction of 
795315Wo* 



1414213 



Let the diagonal be. 16 feet square. 16 x 16 = 256 square 
feet. Double this for the square on the diagonal. 

256 x 2 ^= 5.12 ( 22f f 
4_ 
42 112 

_2 84 

44~ 28 

This, reduced to square forty-fourths, is 996 x 996 = 99201 6 
Subtract the square of the numerator, 28 x 28 = 784 



Divide this by the square of 44 = 

512 reduced to 2048 == H^Vs 7 - 6 - 
2* ~B 



991232 



= 512. 



18 



GEOMETTIY 



The square root of this is Agf f, being equivalent to 22 
feet, 7 inches, f %$ of an inch on a side of the square. 



The Square described on the Diagonal of a Given Square 
is Equivalent to Double the Given Square. 

Let E H F G be a square described on E H, and ABC 
D a square described on the diagonal, E F; the triangle, E 

H F, being right-angled and 

isosceles, you have EF = 

EH+HP=2EH. Hence, 
the area of a square is equiv- 
alent to double the area of 

the diagonal. 

When four magnitudes are 

in proportion, the product 

of the two extremes is equal 
to the product of the two 
moans. 

If four magnitudes are in proportion, they will be in pro- 
portion if taken inversely. 

Equimultiples of any two magnitudes have the same 
ratio as the magnitudes themselves. 

If there be four proportionate magnitudes, and four other 
proportionate magnitudes having the antecedents the same 
on both, then consequents will be proportional. 

As the sum of the one side of a square is to the sum of 
the three sides so is the square of half the sum of the one 
side to three-quarters the area of the square ; for example, 
let the diagonal be 300 feet on a side. 

300: 900:: 150: 67500; 
and if 67500 equals three-fourths the area of the square, 




MENSURATION — TEIG'ONOMETE Y . 



19 



90000 equals the area. Changing the places of the mem- 
bers of the equation, we have 

67500: 22500:: 900: 300. 

And 180000 square feet being the area of double the 
diagonal or the square on the diagonal, we have 

135000 : 45000 : : 1272f f f : 424||| ; 

consequently, the side of a square is to the side of a diagonal 

as 2715288960000000 is to 1919999236496968^ 

nearly, because there is no common measure for the two, 
unless it is the square of the side, as follows : 

The square of 300 = 90.000. 
The square of 424| \\ = 180.000. 



Two Sides of a Right- Angled Triangle Given to Find the 

Other. 
Let A B C D be a square of 100 feet on a side. 

The sides, A K, I K, of the right-angled triangle, A I K, 
are each equal, and twenty-five feet each ; and the square 
root of the sum of the two sides equals the hypothenuse, A I, 
as follows : 





25 




25 




125 




50 




625 




625 




1250 (35f$ 




9 


65 


350 


5 


325 


70 


25 




20 TRIGONOMETRY. 

The sides, A I, E I, of the right-angled triangle, E I A, arc 
each 35§(j, and the square root of the sum of the two sides 
squared equals the side, A E, viz. : 





35;,/ 


35 


. 


CO 


25 




175 


175 


50 


105 


70 


50 


12 — 35 


70 ) 876 


2500 


12 — 35 


70 




1250 


175 




1250 


140 




2500 ( 50 


35 




2.") 





00 

The sides, E J and II J, each fifty feet, being squared, the 
square root of the sum of the two is equal to the diagonal 
EH; and the side of the Bquare, E GF1I 70 ] \ [j, and the two 
sides E G and F G 70] \% being squared, the Bquare root of 
the sum of the two equals 100, the side of the Bquare ABC 
D, this fraction \\^ is a little over, it being aboul | \\ 

of 100. 

Note. — There are some numbers the sum of whose squares being 
a perfect square leave no remainder or fraction. Such are 3 and 4, the 
sum of whose squares is 25, and the Bquare root 5; therefore the hy- 
pothenuse is 5; and if those numbers be multiplied by other numb 
each of the same, the products will be the sides of true right-angled 
triangles. Multiplying them by 2 gives 6, 8, and 10, which arc Q 
by builders in laying out corners. 

Example.^- Suppose G B to be 4 yards in length, and B F 
to be 3 yards in height ; then the square of G B is 16 yards, 
and the square of B F is 9 yards, and the sum of their 
squares is 25 yards. 



GEOMETRY. 



21 



The square root of 25 yards is 5 yards, which is the length 
of the hypothenuse. 



A Regular Polygon is One which is both Equilateral and 
Equiangular. 

A regular polygon may have any number of sides ; the 
equilateral triangle is one of three sides; the square is one 
of four. 

To inscribe in a circle a regular hexagon, let the circle be 
one hundred and twenty- 
eight feet diameter. Be- 
ginning at a point, B, 
apply the radius, B O, 
six times as a chord to 
the circumference, and 
you will form the regu- 
lar hexagon, BCDE 
FA. Draw, O H per- 
pendicular to one of 
its sides ; the area of 
the polygon is equal to 




Fig. 8. 



iOH multiplied by the perimeter. Now let the arcs which 
are subtended by the sides of the polygon be bisected, and 
new polygons formed ; the limit of the perimeter is the cir- 
cumference of the circle. 

The area of the right-angled triangle, B O C, is equal to 
a rectangle 27f^ X 64 = 1773 t 6 -q, being the one-sixth of 
the area of the polygon, which is equal to a rectangle 96 X 
110 T 8 o% = 10641-^ feet. 

To find the area of a triangle when the base and altitude 
are given, multiply the base by the altitude, and take half 
the product, or multiply one of these dimensions by half 
the other. 



22 



GEOMETRY. 



The circumferences of circles are to each other as their 
radii, and the areas are to each other as the squares of their 
radii. 

The circumferences of circles are to each other as their 
diameters, and their areas are to each other as the squares 
of their diameters. 

The circumference of the circle is the limit of all in- 
scribed polygons ; in fact, the circle is but a regular polygon 
of an infinite number of sides. 

If a regular hexagon be inscribed in a circle, its Bide will 
be equal to the radius. 



The Area of a Circle is Equal to the Product of Half the 
Radius by the Circumference. 

Let ACDE be a circle whose centre is O and radius 
O A ; then will area OA = ^OAx cir. O A. 

For inscribe* in the circle 
any regular polygon, and 
draw OF perpendicular to 

one of its sides. The area 
of the polygon is equal to 
D A O F multiplied by the pe- 
rimeter. Now let the arcs 
which are subtended by the 
sides of the polygon be bi- 
sected, and new polygons 
formed, as before. The limit 
£' of the perimeter is the cir- 

cumference of the circle ; the limit of the apothegm is the 
radius O A, and the limit of the area of the polygon is 
the area of the circle passing to the limit ; the expression 
for the area 




GEOMETRY. 23 

is area OA = |OAx cir. O A ; 

consequently, the area of a circle is equal to the product of 
half the radius by the circumference. 

The problem of the quadrature of the circle, as it is 
called, consists in finding a. square equivalent in surface to 
a circle, the radius of which is known. Now, it is proved 
that a circle is equivalent to the rectangle contained by its 
circumference and half its radius ; and this rectangle may 
be changed into an equivalent square by finding a mean 
proportional between its length and its breadth. To square 
the circle, therefore, is to find the circumference when the ' 
radius is given ; and for effecting this it is enough to know 
the ratio of the diameter to the circumference. 

Archimedes showed that the ratio of the diameter to the 
circumference is included between 3y§ and 3 if-, hence 3^- 
or 2 T 2 . 

Metius, for the same quantity, found the much more accu- 
rate value, fff. 

Proposition, Theorem, and Calculation of the Limit of the 

Circle. 

Let A B C be a circle, of which the centre is D and the 
diameter, A C, 128 feet. 

In the circle, A B*C, apply the straight line, E F, equal to 
the radius, D C ; draw also D F, D £, and B F. It is evi- 
dent that the arc E B F is one-sixth of the circumference. 

The equilateral triangle, E D F, is the one-sixth part of 
a six-sided polygon, the perimeter of which is three times 
the diameter of the circle, viz., 384 feet. 

The line G F, or half of E F, is 32 feet, but the line B F is 
33.128837773122657-,% ; and B F is the side of a twelve- 
sided polygon drawn inside the circle : it is evident that 
as you increase the sides of the polygon you approach the 



24 



GEOMETRY. 



circumference of the circle. Continuing the increase to a 
polygon of three million one hundred and forty-five thousand 
seven hundred and twenty-eight sides (3,145,728), you pro 
ceed as follows: the hypothenuse,DF, of right-angled triangle 




D6F, being sixty-four feet, and the base, G F, thirty-two, 
the square root of the difference of the squares of the same 
is equal to the perpendicular D G, 55.425625842204073 ; 
and subtracting D G from D B gives the base line G B of 
right-angled triangle G B F, and the square root of the sum 
of the squares of G F and G B gives the dimensions of the 
line B F, therefore the half of B F is the base line of a right- 
angled triangle of a twenty-four-sided polygon, and so con- 
tinue until you reach a polygon of 3145728 sides. 



TRIGONOMETRY. 25 



Calculation of Right-angled Triangle in Polygon of 

12 Sides. 



Example. 


30.72 ( 55.425625842204073 
25 


32 
32 


. 105 572 
5 525 


64 

96 


1104 4700 
4 4416 


1024 


11082 28400 
2 22164 




110845 623600 
5 554225 




1108506 6937500 
6 6651036 


64 
64 


11085122 28646400 
2 22170244 


256 
384 


110851245 647615600 
5 554256225 


4096 
1024 


1108512508 9335937500 
8 8868100064 


3072 


11085125164 46783743600 
4 44340500656 




110851251682 244324294400 
2 221702503364 




1108512516842 2262179103600 
2 2217025033684 




110851251684404 451540699160000 
4 443405006737616 




11085125168440807 81356924223840000 
7 77595876179085649 




110851251684408143 376104804475435100 

3 332553755053224429 



26 



TRIGONOMETRY. 



84. 

55.425G25S42204073 



8.574374157795927 



8.574374167705927 
r43741577l 

60020619104671489 
17148748316691864 
77169367420163843 
42871870788979636 
77169867420163343' 
60020619104571489 
60020619104671489 
42871870788979636 
8674374157796927 
34297496631183708 
60020619104671489 
26723122473387781 
34297496631183708 
60020619104571489 
42871870788979635 
68594993262367416 

73.519892197878612448950577789329 

1024. 

1097.5K)S92197S7S61244S9505777S9329 



TRIGONOMETRY. 



27 



10.97.51.9 



1.92.19.78.78.61.24.48.95.05.77.78.93.29 ( 33.1288377731 

[22657 T % 



63 
3 

661 
1 

6622 

2 

66248 



197 
189 



851 
661 



19098 
13244 



662568 
8 

6625763 
3 



585492 
529984 

5550819 
5300544 



25027578 
19877289 



66257667 515028978 
7 463803669 



662576747 5122530961 
7 4638037229 



6625767547 

7 

66257675543 
3 

662576755461 
1 

6625767554622 

2 

66257675546242 

2 

662576755462446 



6625767554624525 
5 

6625767554624*5307 
7 



48449373224 
46380372829 



206900039548 
198773026629 



812701291995 
662576755461 



15012453653405 
13251535109244 



2 ) 33.128837773122657.6 
16.564418886561328.8 



176091854416177 
132515351092484 

4357650332369378 
3975460532774676 

38218979959470293 
33128837773222625 

509014218624766829 
463803728823717149 



28 TRIGONOMETRY. 



Calculation of Right-angled Triangle in Polygon of 

24 Sides. 



Example. 



16.564418886561328A 
16.564418886661328A 

1325163510924906 
33128837773122656 
49693256659683984 
1656441888656132 
99386513319367968 
82822094432806640 
99386513319367968 
132515351092490624 
132515351092490624 
132515351092490624 
16564418886561328 
66257675546245312 
66257675546245312 
99386613319367968 
82822094432806640 
99386513319367968 
16564418886561328 

13251535109249062 
13251535109249062 

274379973049469651748266523621708 



TRIGONOMETRY. 



29 



121 
1 

1228 



64 
64 

256 
384 

4096. 
2 74.37 99 73 04 94 69 65 17 48 26 65 23 62 17 08 

38.21.62.00.26.95.05.30.34.82.51.73.34.76.37.82.92 ( 61.819252882 
36 

221 

121 



[500370 T 3 o 



10062 
9824 



12361 23800 
1 12361 

123629 1143926 
9_ 1112661 

1236382 3126595 

2_ 2472764 

12363845 65383105 

5_ 61819225 

123638502 

2_ 

1236385048 



356388030 
247277004 



64. 

61.819252882500370.3 

2.180747117499629.7 



10911102634 

9891080384 



12363850568 

8 

123638505762 

2_ 

1236385057645 

5_ 

1236385057650003 

3_ 

12363850576500067 

7_ 

123638505765000740 



102002225082 
98910804544 



309142053851 
247277011524 
6186504232773 
6181925288225 



4578944548347637 
3709155172950009 
86978937539762882 
86546954035500409 
43198350426241392 



3* 



30 TRIGONOMETRY. 



2.180747117499629^ 
2.1S0747117499G29A 

19626724057496661 
4361494234999258 
13084482704997774 
19626724057490061 
19626724057496661 
8722988469998516 
15265229822497403 
2180747117499029 
218074711749: 
15265229822497403 
8722988469998516 
15265229822497403 
17445976939997032 
2180747117499629 
4301494234999258 

1520522982249740.3 
1526522982249740.3 

4755657990482943744934779637122 



2 ) 16.707352604166603.7 



8.353676302083301.8J 



TRIGONOMETRY. 31 

2 74.37 99 73 04 94 69 65 17 48 26 65 23 62 17 08 
4.75 56 57 99 04 82 94 37 44 93 47 79 63 71 22 

2.79.13.56.31.03.99.52.59.54.93.20.13.03.25.88.30 ( 16.70735260416 
1 [6603 T V 



26 179 
6 156 



327 2313 

7 2289 



33407 245631 
7 233849 



334143 1178203 
3 1002429 



3341465 17577499 
5 16707325 



33414702 87017452 
2 66829404 



334147046 2018804859 
6 2004882276 



33414705204 139225835493 
4 133658820816 



334147052081 556701467720 
1 334147052081 



3341470520826 22255441563913 
6 20048823124956* 



33414705208326 220661843895703 
6 200488231249956 



334147052083326 2017361264574725 
6 2004882312499956 



33414705208333203 124789520747698830 
3 100244115624999609 



32 



TRIGONOMETRY. 



Summary of Calculating" the Angles of Polygons from 
12 to 3145728. 



Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 

Base . 
Perpendicular 

Hypothenuse 

Base . 

Perpendicular 

Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 



Polygon of 12 Sides. 

32. feet, 
55.425625842204Q73, 

64. 

8.574374157795027, 
32. 
33.128837773122657^. 

Polygon of 2J f Sid* & 

16.564418886561328^1 
61.8192i 

G4. 

2.180747117499629^, 
16.56441888656] 
16.707352604166603^ 

Polygon of £8 (Ski 

. 8.353676302083302, 
. 63.452471127923* 

. 64. 

.547528872076134, 
. 8.353676302083302, 

. 8.371600541458312. 

Polygon of 06 Sides. 

4.185800270729150, 
63.862971087270624, 
64. 

.137028912729376, 
4.185800270729156, 
4.188042601187346. 



TRIGONOMETRY. 



33 



Base . 

Perpendicular 
Hypotlienuse 

Base . 

Perpendicular 
Hypotlienuse 



Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypotlienuse 



Polygon of 192 Sides. 

2.094021300593673, 
63.965733598487401, 
64. 

.034266401512599, 
2.094021300593673, 
2.094301648190307. 

Polygon of 384 Sides. 

1.047150824095153J, 
63.991432826211954, 
64. 

.008567173788046, 
1.047150824095153^, 
1.047185869303952. 



Base . 

Perpendicular 
Hypotlienuse 

Base . 

Perpendicular 
Hypotlienuse 



Base . 

Perpendicular 
Hypotlienuse 

Base . 

Perpendicular 
Hypotlienuse 



Polygon of 768 Sides. 

.523592934651976, 
63.997858170713670 T 6 o, 
64. 

.002141829286329-^, 
.523592934651976, 
.523597315358052 T % 

Polygon of 1536 Sides. 

.261798657679026^, 
» 63.999464540438441!, 

64. 

.000535459561558*, 

.261798657679026^, 
.261799205269004. 

C 



34 



TRIGONOMETRY. 



Base . 

Perpendicular 

Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 



Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 

Hypothenuse 



Base . ' 

Perpendicular 

Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 



Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 



Polygon of 3072 Sides. 

.130899602634502, 
63.999866134969611 T fi o 
64. 

.000133865030388^ 

.130899602634502, 

.130S99671083302 T 8 - 

Pohjgon of GL$4 Sides. 

.065449835541651^ 
63.9999665337336 

64. 

.000033466266347^ 
.065449835541651^ 
.065449844097753^, 

Polygon of 12288 Sides. 

.032724922048876^ 
63.999991633432944^ 

64. 

.000008366567055^ 

.032724922048876^ 
.032724923118388^ 

Polygon of 24576 Sides. 

.016362461559194^ 
63.999997908358182^ 

64. 

.000002091641817^ 
.016362461559194^ 

.016362461692883. 



TRIGONOMETRY. 



35 



Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 



Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 



Polygon of Jf9152 Sides. 

.0081812308464411, 
63.999999477089543 T 4 o, 
64. 

.000000522910456/o, 

.008181230846441, 

.008181230863152 T %. 

Polygon of 98304 Sides. 

.004090815431576^, 

63.999999869272385 T 7 o, 
64. 

.000000130727614^, 
.004090615431576 T 3 o, 
.004090615433665^. 



Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 



Polygon of 196608 Side*. 

.002045307716832^, 



63.999999967318096/o, 
64. 



.000000032681903,%, 
.002045307716832^, 
.002045307717093 T V 



Polygon of 398216 Sides. 



Base . 

Perpendicular 

Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 



.001022653858546fg, 
63.999999991829524^, 
64. 

.000000008170475 T 9 o, 
.001022653858546f^, 
.001022653858579 T 4 o. 



36 



TRIGONOMETRY. 



Polygon of 786432 Sides. 



Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 

Hypothenuse 



Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 



.000511326929289^, 

63.999999997957381, 
64. 

.000000002042619, 

.000511326929289^, 
.000511326929293^. 



Polygon of 1572864 Sides. 

.000255663464646 
63.99999999 
64. 

.000000000510654^, 
.0002556634641 

.000255663464647, 

Polygon of 8145728 Si 

.000127s317: > >2: > >23,V 9 IJ , 
63.999999999872336^, 
64. 

.000000000127663 , : 



.0001278317 
.00012783173232 



Base . 

Perpendicular 
Hypothenuse 

Base . 

Perpendicular 
Hypothenuse 

Now, the line drawn from the centre to an angle of the 
polygon, the perpendicular let fall on one of the equal rides, 
and half this side, form a right-angled triangle, in which 
there are known the base, which is half the side of the 
polygon, and the angle at the vertex, hence the perpendic- 
ular can be obtained. 

The apothegm or perpendicular of the polygon of 3145728 
sides being 63.999999999969646^, and the perimeter 402. 
123859659302850 T V 



GEOMETRY. 37 

Then the half of the perpendicular, viz., 31.9999999999- 
84823 T 3 o x402.123859659302850 r 9 o = 12867.963509091588- 
315, area of polygon. 

Now as 63.999999999969646 T 6 o, the apothegm or perpen- 
dicular of polygon 3145728 sides, is to its perimeter so is 64 
the limit to the circumference of the circle, viz., 63.99999- 
9999969646 T 6 o : 402.123859659302850 T 9 o : : 64 : 402.1238596- 
59493567. 

Therefore 402.123859659493567 is the circumference of 
a circle 128 feet in diameter. 

The diameter of a circle is to its circumference as the 
square of the radius to the area of the circle. 

128 : 402.123859659493567 : : 4096 : 12867.963509103794144. 

Therefore 12867.963509103794144 is the area of a circle 
128 feet in diameter. 

And the ratio is 1 to 3.141592653589793 T ¥ 8 . 

The diameter of a circle is to the circumference in the 
ratio of 1 to 3.141592653589793 T ^ 3 3. 

Therefore as 402.123859659493567 is to 128 so is the 
circumference to the diameter. 

To Find the Diameter of a Circle. — Divide the circumfer- 
ence by 3.141592653589793^^, and the quotient will be the 
diameter. For a short and near calculation, multiply the 
circumference by 113, and divide by 355. 

To Find, the Circumference of a Circle. — As 128 is to 402.12- 
3859659493567 so is the diameter to the circumference, that 
is, multiply the diameter by 402.123859659493567, and 
divide by 128, the product will be the circumference ; and 
to shorten the calculation, multiply by 355, and divide by 
113, which gives the answer nearly. 
4 



38 GEOMETRY. 

To Find the Area of a Circle. 

Kule 1. — Multiply half the circumference by half the 
diameter, and the product will be the area. 

Eule 2. — Multiply the square of the diameter by the deci- 
mal ,785398163397448^VA> and tbe product will be the 
area; and to shorten the calculation, multiply by .7854, which 
will give the area nearly. 

Rule 3. — Multiply the square of the circumference by the 
decimal .0795774715459476614 +, and the product will be 
the area; and to shorten the calculation, multiply by .07958, 
which will give the area nearly. 

Rule 4. — Multiply the circumference by the radius, and 
divide the product by 2. 



Area of the Circle by Per Cent. 

The area of a circle can be determined by weight or cent- 
age. Cut from sheet-metal a square and circle, the diameter 
of the circle equal to the side of the square ; weigh them, 
and take the difference. On trying the experiment, the re- 
sult was as follows : 

Weight of square, . . . 238 grains. 
Weight of circle, . . . 187 grains. 

The circle being 21 T 4 % per cent, less than the square, 
therefore, by squaring the diameter of a circle, and sub- 
tracting 21 -^ per cent., will give the area of the circle ; for 
example : 

64 x 64 = 4096 

Less 21 T 4 °o per cent. 879 

3217 



GEOMETRY. 



39 



THE SQUARE OP THE CIRCLE. 

J B 




Fig. 11. 

The circle, 64 feet diameter, circumference 201.0619298- 
29746783 T 6 2 4 8, area 3216.990877275948536, equals a rectan- 
gle 32 x 100.530964914873391 T 9 3 V 

The square, ABCD, sixty-four feet on a side, equals in 
area 4096 feet. 



The square, R J L K, 45f Jf + X 45?ftft, or 45|| x 45|f , 
that is, 45 x 45, and f § of 45 on the two angular sides, 
equals in area 2048 feet. 



40 





GEOMETRY. 




45.218 


&-U 


45 


45.218 


45.1a 


23 


361 744 


225 


135 


45218 


180 


90 


9043 6 


11.45 


90)1035(11 


226090 


11. 


90 


180872 


2048 


135 


2044667 524 




90 

45 



The square, EFGH, 55.424+ x 55.424+, or 55^ X 
55 T 4 T 7 3, in area 3072 feet, being three-fourths of the area 
of A BCD. 

The square, E O G P, 48 x 55.424 +,or 48 x 55^, is 

509 ] " 
equal to the area of the hexagon 2660.- rJ ]i) - feet. 

The square, E F G II, including the dotted lines, is the 
equivalent of the circle, and the same ana being 56.71 
282fHimit! x 68.7186288ff|}|4| in area 3216- 

.990877275948536=a rectangle of 32 x 100.530964914873- 

The triangle, E G L, 55.424 + base, and 48 feet high, 

equals in area 1330f§^. 

509 
The hexagon, REMLNG; area, 2660 glSl. 



The square of the diameter of any circle is to its area as 
the perimeter of a square, described on the diameter of the 
circle, to its circumference, or the converse of the proposition. 
The area of any circle is to the square of its diameter as the 
circumference of the circle to the perimeter of a square de- 
scribed on its diameter. These facts may be demonstrated on 
any hypothetical data taken to represent the value of the 



GEOMETRY. 



41 



circle; as, 4096 : 3216.990877275948536 : : 256 : 201.0619298- 
29746783 #*• 

THE SQUARE OF THE CIRCLE. 




Fig. 12. 



Let the diameter of this circle (Fig. 12) be 8 inches. 
The circumference is 25.132741228718347^. 
The area of both is 50.265482457436695fjf . 
This circle and square are equal. The square 



is 



7.089815403, and &yWWW% of 7.089815403 on two 
angular sides of the square. 
4* 



42 



GEOMETRY. 



1408 
8^ 
14169 
9 



128 : 402.123850659493567 : : S : 25.132741228718347 
50.26.54.82.45.74.36.69.5fif ( 7.089815403 
49 

12654 

11264 



139082 
127521 



141788 
8 


1156145 
1134304 


1417961 


2184174 
1417961 


14179625 
5 


76621336 
70898125 


141796304 
4 


667185216 


14179630803 513( 

3 42538892409 



14179630806 



8820643466 



14179630S06 



70S9S15403 

882nii4:: 

42538892418 

21269446209 
L612 

1117 

5671 
56718523224 

625J L0321733 

56718523224 

581 v 

56718523224 



7089815403 

7089815-103 

21269446209 
28359261612 
35449077015 
7089815403 
56918523224 
83S08338627 
56718523224 
49628707821 

50265482448616052409 

4410321733 

4410321733 

60265482457436695875 



321 

14179630 

45620551581 

4253SX92418 

30816591630 
59261612 

24573300186 

14179630S06 

103936693807 

992574 K 

46792781 059 
42538892418 



42538892418 
42538892418 



MENSURATION OF SURFACES, 



43 



Measurement by Parallel Lines. 

To measure any figure, as a long irregular, curved, rec- 
tangle, square, or circular, by means of parallel lines drawn 
perpendicular, or at right angle to its greatest length ; the 
greater the number of lines and spaces, the more perfect the 
measure. Divide the aggregate length of the lines by the 
number of spaces for the mean, and multiply that by the 
greatest length of the figure, and the answer will be the 
area. 

Example First. — Let A B C D, Fig. 13, be'a square, 32 
feet; draw 21 lines perpendicular, as marked, extending 
them across the square, equal distances apart; the aggre- 
gate length of lines is 497f feet ; divided by the number of 
spaces 22 = 22 W; this multiplied by the greatest width, 
viz., 45.254 +, equals 1023.872, the area of the square; the 
exact area is 1024. 

Example Second.— Draw 21 lines perpendicular to D E 
B, Fig. 13, triangle, DEBC; the aggregate length of the 
lines is 249 feet; di- 
vided by 22 spaces == 
ll 3 7 o ; multiplied by 
the length, DEB, 45. 
254 + =512.193; the 
correct or exact area 
is 512 feet. 

Example Third. 

— The chord of one- 
fourth of a circle, the 
radius 32 feet, that 
is, D E B F, Fig. 13, 
divided in the same 




Fig. 13. 



manner, and the lines aggregating 142-j% feet, divided by 22 



44 MENSURATION OF SURFACES. 



:6. ^;°; multiplied by 45.254+ =293.74 feet area. 



spaces : 

The correct or exact area is 292.247719318987134. 

Example Fourth. — The corner triangle with curved 
side, D F B, divided in the same manner, and the lines ag- 
gregating 106 T % feet, divided by 22 spaces, equals 4.8AS ; and 
multiplied by 45.254 + =219.222 feet area. 

The correct and exact area is 219.752280681012866. 
Example Fifth. — A circle of 32 feet diameter, divided 
into 39 lines and 40 spaces, the lines aggregating 1005 T fi a 
feet, divided by 40 spaces, equals 25^, and multiplied by 
32 = 804.48. 

The correct and exact area is 804.247719318987134. 
Example Sixth. — Let Fig. 14, A BCD, represent a 

sail of the dimensions, viz., AB 
11 \ feet, B C 31 feet, DC 22A feet, 
A D 22 feet. The largest line 
drawn across this will be from 
A to C, 311 feet; divided into 20 
lines and 21 spaces, and the lines 
drawn at right angles to A C, 
aggregate 283^ feet in length. 




Fig. 14. 



10 

283^ + 21=13 ^=423^ 



square feet the area. 

Example Seventh. — Let a hexagon be 32 feet on a side; 
the largest length, or greatest diameter, will 
be G4 feet ; draw 63 lines perpendicular to 
this. The lines will aggregate 1330 feet ; 
divide by 64 spaces; the quotient multiplied 
by 64 gives the same answer, 1330 feet area. 
Let the circle, Fig. 15, be 16 feet in di- 
Fig. 15. ameter; draw 31 lines ; the aggregate length 




MENSURATION OF SURFACES. 



45 




of the lines is 402 feet ; divided by 32 spaces =12j| ; multi- 
plied by 16 = 201 feet area. 

Let Fig. 16, a ring or section of a circle, be 32 feet di- 
ameter, with a blank space 
in the centre 16 feet in di- 
ameter ; draw 63 lines ; the 
aggregate length of the lines 
is 1206 feet; divided by 
64 spaces equals 188-g-f feet; |= 
multiplied by 32 equals 603 \ 
feet area. 

The square 32 X 64 lines 
(counting | of each side 
one) = 2048 feet of lines, 
and the area is 1024 feet. 

Figure 15 201 feet. 

Figure 16 ....... . . . 603 " 

Between Fig. 16 and the square . 220.6 " 

1024.6 " 
In this manner the last two examples can be used as a 
proof or test of the exact contents of the circle, because 
doubling the diameter quadruples the area, and with the 
best instruments for ruling parallel lines an exact fractional 
measure can be obtained ; if with imperfect ones, the above 
results are nearly exact. The calculations are made on a 
scale of 8 inches. 

A quarter-sector of any circle is equal in area to a circle 
of half its diameter. 

To Find the Area of a Triangle ichen the TJiree Sides are 
given. — First. Add the three sides together, and take half 
their sum. 



46 



MENSURATION OF SURFACES. 



Second. From this half sum subtract each side sepa- 
rately. 

Third. Multiply together the half sum and each of the 
three remainders, and the product will be the square of the 
area of the triangle. Then extract the square root of this 
product for the required area. For example, take a trian- 
gle whose sides are 18, 24, 30. 

18 36 36 36 36 

24 18 24 30^ _18 

30 18 12 6 288 

2)72 M 

36 

12 
7776 

6 

46656 
The square root of 46656 = 216 feet area. 

The side or perpendicular of the equilateral triangle given 
to find the other dimension and area. 

Let the large equilateral trian- 
gle be three times the size of the 
small one; then the perpendicular 
of the small triangle will be half 
the side of the large, and the per- 
pendicular of the large triangle 
will be one and a half times the 
side of the small one. 

The side of the small triangle 
is 400 feet. 

The perpendicular of the large 
triangle is 600 feet. 

We cannot give the exact dimensions of the side of the 




Fig. 17. 



TKIGONOMETRY. 



47 



large triangle, or the exact perpendicular of the small tri- 
angle ; but we can give the exact square of the dimension 
of both, as follows : 

The perpendic. of the large triangle, 600 X 600 = 360000. 

" " small " one-third = 120000. 
The square root of 120000 = 346f§£. 
The side of the small triangle, 400 x 400 = 160000. 
u « u « i arge « three times = 480000. 
The square root of 480000 = 692.82+. 

Side of square, D E, 200 X 200 = 40000. 

Side of large square, A B, three times = 120000. 

Side of large square, D B, 600 X 600 = 360000. 

Side of small square, E G, one-third = 120000. 

Therefore, for area of large triangle, A B, 120000 X B D 
360000 = 43200000000, the square root of which equals 
207816.096 +, the area, and for small triangle area equals | 
69282.032+. 

Kule. — For the perpendicular of an equilateral triangle, 
multiply the side by the decimal .866025. 

Rule. — For the side of an equilateral 
triangle, multiply the perpendicular by 
1.1547. 

To find the distance from A to B, when 
B only is accessible. (Fig. 18.) 

Lay off a square with B D in range with 
the object, and stake each corner, say 12 
feet square ; extend the line D E to F in 
range with stake C and the object, say, for 
example, 4 feet, then as E F : E C : : B C : 
B A, or 4 : 12 ; : 12 : 36. 




Fig. 18. 



48 



MENSURATION OF SURFACES. 



Table of Polygons. 



Names. 




Angle at 
Vert 


le at 

Centre. 


Areas. 


Trigon or Equilateral 
Triangle 


3 
4 
5 
6 

7 

8 

9 

10 

11 

12 


60° 
90° 

108° 

120° 
128° 34' 29" 

135° 

140° 

144° 
I47°16 / 36 // 

150° 


120° 

90° 
72° 
60° 
31° 25' 71" 
46° 

36° 
;'64" 


0.43:- 

<)000 

1.7204774 

S0762 

,1124 

1271 

11.1!", 


Tetragon or Square... 
Pentagon 


Hexagon 


Heptagon 


Octagon 


Nonagon 


I )cc;ii(<>n 


Undecagon 


L)o(leca <r on 





To find the area of any regular polygon, multiply 
gcther one of its Bidea — that is, one of its sides and 

multiply the product by the area, as above, and the quo- 
tient will be the area, unless the .-ides are decimals, when it 
will not answer. 

To find the area of any parallelogram, multiply any side 
by the perpendicular height. 

The diagonal of any parallelogram divides it into two 
equal triangles, and four diagonals divide it into four trian- 
gles of equal an 

The four angles amount to four right angles, or 3G0°. Any 
two diagonally oppo.-itc angles are equal to each other, and 
having one angle, the other three can readily be found. 

To find the area of any figure inclosed in four straight 
lines, draw two diagonals from the angles intersecting each 
other, multiply together the two diagonals and the natural 
sine of the least angle formed by the intersection, and divide 
the product by 2. 

Or, draw a diagonal from opposite angles, and two perpen- 
diculars from the vertex of opposite angles falling upon the 



MENSURATION. 49 

diagonals; multiply the diagonals by the sum of the two 
perpendiculars, and half the product will be the area. 

To find the diameter of a circle of the same area as a 
given ellipse, multiply together the two diameters, and take 
the square root of product 12 x 20 = 240 = 15^. 

To Find the Area of an Ellipse. 

Multiply the two diameters together ; multiply the prod- 
uct by .7854. 

Example.— 12 x 20 x 7854 = 188.4960. 

The area of an ellipse is a mean proportional between the 
area of two circles described on its two diameters, therefore 
it may be found by multiplying together the areas of those 
two circles, and taking the square root. 

To Find the Area of a Long, Irregular Figure. 

Divide the space into equal distances ; the more spaces 
the more correct. Measure these lines, add them together, 
and divide the sum by the number of lines for the mean 
breadth; then multiply that by the length of the figure, 
and the product will be the area. 

Cylinders. 
To find the surface, multiply the circumference by the 
perpendicular, to which add that of the ends. 

To find the solidity, multiply the area of one end by the 
perpendicular ; the solidity of a cylinder is three times that 
of a cone of the same base and height. 

To find the solidity of any pyramid or cone, whether reg- 
ular or irregular, right or oblique, multiply the area of its 
base by one-third of its perpendicular height. Every pyr- 
amid or cone has one-third of the solidity of either a prism 
or a cylinder, having the same area or base and the same 
5 D 



50 MENSURATION. 

height, and one-half that of a hemisphere of the same base 
and height; a cone, hemisphere, and cylinder of the same 
base and height have solidities, as 1, 2, 3. 

To mid the surface of a right pyramid or right cone, mul- 
tiply the outlines of its base or circumference by the slant 
height; take half the product. This will give the surface of 
the sides, and, if required, that of the base; the slant height 
must be measured from the apex to the middle of the base. 

To find the solidity of any prismoid, add together the 
areas of the two parallel surfaces and four times the ai 
of the section taken half-way between them, and parallel to 
them. Multiply the sum by the perpendicular distance be- 
tween the two parallel Bides, and divide the product by 6. 

To find the solidity of a sphere, cube its diameter; mul- 
tiply said cube by .5236, or cube [ts circumference, and mul- 
tiply by .01689, or multiply its surface by its diameter, and 
divide, by 6 ; the solidity of a sphere is two-thirds that of 
circumscribing cylinder, or .5300 of that of its circumscrib- 
ing cube. 

To find the surface of a sphere, square its diameter ; mul- 
tiply said square by. 3183. The surface of a sphere is equal 
to four times the area of its great circle, or to the area of 
a circle whose diameter is twice as great as that of the 
sphere. 

For the area of a square equal to an equilateral triangle, 
square the side, and multiply the quotient by the 'decimal 
.4330. 

For the side of a square equal in area to a triangle, mul- 
tiply the side of triangle by .658. 

For the side of a triangle, multiply the side of the square 
by .15197. 



GEOMETRY. 51 

To Find the Length of an Arc of a Circle containing any 
Number of Degrees. 

Multiply the number of -degrees in the given arc by 
0.008726646259971| |§|g, and the product by the diameter 
of the circle. 

For since the circumference of a circle, whose diameter 

is 1, is 3.141592653589793^, it follows that if 3.141592- 

653589793 T 6 2 3 8 be divided by 360, the quotient will be the 

, . ■ 3.141592653589793^ 
length oi an arc of 1 degree, tnat is, ^^ — 

= 0.008726646259971-J§g£J = arc of one degree to the di- 
ameter 1. 

If this be multiplied by the number of degrees in a given 
arc, the product will be the length of that arc in the circle, 
whose diameter is 1. If this product be then multiplied by 
the diameter of any circle, the product will be the leugth 
of the arc in that circle. 

To find the length of an arc of 1 degree, the diameter 
being 128 feet. Ans. 1.117010721276371^. # 

To find the length of an arc of 1 degree, the diameter 
being the earth's diameter, 41846930.638-f § feet. 

Ans. 365183.360^ feet. 

For the side of a square equivalent to a circle, multiply 
the diameter by .08862269;* nearly. 



The Earth's Equatorial Radius. 
251081583.833 inches. 
20923465.319^ feet. 



The Earth's Equatorial Diameter. 
502163167.666 inches. 
41846930.638}£ feet. 



52 GEOMETRY. 

7925.555 statute miles. 

6875|§^f£f§| geographical or nautical miles. 

m 237879908817733 . g fi2 fWrppq 
402123859G59493TGT Ue & 2 etb< 

114 degrees, 35 minutes, 29 seconds, -j% + . 



The Earth's Circumference at the Equator. 

1577592118.442| inches. 

131466009.870 feet. 

360 degrees. 

24898.865A statute miles. 

21600 geographical or nautical miles. 

(59.y 6 o : o statute miles to 1 degri 

Area of the circumference equals a square of 7023 statute 
miles. 

Area of the surface equals a square of 14048 statute 
miles. 

Calculation of the Diameter and Circumference of the 
Earth in French Metres. 

128: 402.1238596:)!) 493567 : : 12754046: 40069120. 

12754646 metres in diameter. 

40069120 metres in circumference. 

The one-fourth of the above, supposing it to be even forty 
millions, or the quadrant and the distance from the equator 
to the north pole, is adopted by the French Government 
the fundamental standard for the metrical system of weights 
and measures. 

The quadrant is divided by them into 10000000 equal 
parts, one of which is taken for one metre ; and this unit is 
the foundation for all their weights and measures. 



THE EARTH. 53 

The Earth. 

The earth is a planet in all respects similar to Venus and 
Mars, its nearest neighbors, which planets probably are in- 
habited the same as the earth. The form of the earth is not 
that of a sphere, but of an oblate spheroid, like possibl} 7 all 
of the planets. The eccentricity of the earth's orbit amounts 
to 0.1677110, but is subject to a small diminution, about 
0.000041 in a period of 100 years, and this continued, must 
eventually result in a change of the form of the earth's or- 
bit from an ellipse to a circle, unless some unknown external 
cause reacts after a period and changes or restores it again 
to its original condition. 

The earth's heat increases at the rate say 100° a mile, 
many miles into the interior. At a distance of 12 miles into 
the interior, we have a red-hot heat ; at a distance of 100 
miles, the temperature will be so great as to melt the mate- 
rials composing the crust of the earth. In fact, we have every 
reason to suppose that the crust has been cooling gradually 
for hundreds of thousands of years, and that our earth is 
nothing but the scoriae from a fused mass from velocity, at- 
traction, condensation, and gravitation. 

We know that the earth is nearly a sphere by the appear- 
ance of a ship at sea ; first the topmast looms up in the dis- 
tance, then next the lower rigging, then the hull, when 
finally the whole and every part of the clipper-built vessel 
appears in all her beauty, walking the waters like a thing 
of life; also by the varying appearances of the constella- 
tions as we proceed northward or southward, and other indi- 
cations. After the sun has set below the horizon and disap- 
peared from the view of the inhabitants at the base of a 
high elevation, it can again be observed by ascending to the 
summit. 

The earth turns on its axis in 23h. 56m. 4.09s., conse? 
5* 



54 



TABLES. 



quently, we are travelling, by this diurnal motion, at the rate 
of 1040 miles per hour on our whirling vehicle the earth, in 
the direction from west to east in a circle, while at the same 
time we are travelling in an elliptical direction at the mean 
rate of 66.168 miles per hour, — a double motion somewhat 
similar to that of a top turning round, at the same time 
passing over the ground in a curved line. 



The following Table of the Lengths of Days in Different 
Latitudes is from M'adler. 



o 


' 


11 01 


o 


' 


Hoi 








12 


65 


48 


22 


16 


44 


13 


66 


21 




30 


48 


14 


66 


32 


-1 


41 


24 


15 


67 


23 


1 mo. 


49 


2 


16 


69 


51 


2 u 


54 


31 


17 


73 


40 


3 " 


58 


27 


18 




11 


4 " 


61 


L9 


1!) 


-l 


5 




63 


23 


20 


90 





6 " 


64. 


50 


21 

• 









The 8646 hours which make up a year are according to 
the same authority. 



At the Equator. 

4348 hours day. 

852 " twilight. 
3446 " night. 



At the Poles. 
4389 hours day. 
2370 " twilight. 
1887 " night. 







TABLES. 00 


Table Showing 


Difference of Time at 12 o'clock (noon) at 






New York. 


New York . . 


12.00 Noon. 


Boston . . . 12.12 P.M. 


Buffalo . . . 


11.40 A. M. 


Quebec . . ". 12.12 " 


Cincinnati . . 


11.18 


a 


Portland . . 12.15 " 


Chicago . . . 


11.07 


a 


London . . . 4.55 " 


St. Louis . . 


10.55 


a 


Paris .... 5.05 " 


San Francisco . 


8.45 


a 


Rome . . . 5.45 " 


New Orleans . 


10.56 


tt 


Constantinople 6.41 " 


Washington 


lt.48 


a 


Vienna . . . 6.00 " 


Charleston . . 


11.36 


a 


St. Petersburg 6.57 " 


Havana . . . 


11.25 


u 


Pekin, night . 12.40 A.M. 


Time Table. - 


— 60 seconds = 


= 1 minute ; 60 minutes = 1 


hour; 24 hours 


= 1 day. 




Measure or 


Division of the Circle. 


60" seconds 






= r minute, 


60' minutes 






= 1° degree, 


30° degrees 






= I s sign, 


90° degrees 






= 1 quadrant, 


12 signs, or 360 


degrees, 


= 1 circumference. 



The circumference of the globe, like every other circum- 
ference, is divided into 360 equal parts, called degrees; each 
degree is divided into 60 equal parts, called miles or minutes. 
Three miles are called a league. 



Geographical or Nautical Measure. 

6 feet = 1 fathom, 

110 fathoms, or 660 feet, = 1 furlong, 

120 fathoms = 1 cable's length, 

6086.389| feet = 1 nautical mile, 



56 TABLES. 

3 nautical miles = " 1 league, 

20 leagues, or GO geographical miles, = 1 tk 
3G0 decrees the earth's circumference. 



Gunter's Chain. 
7.92 inches = 1 link, 

100 links = 4 rods, or 22 y 



Long Measure. 

12 inches = 1 foot, in. ft. , yd. rds. fur. 

3 feet = 1 yard, 

r>.l vanls 1 rod, pole, or perch, 1 

40 rods == 1 furlong, 220 40 

8 furlongB - 1 rtatute mile, I ^8 

3 miles 1 league. 





Square 


Measure. 






144 inches 


= 


! 


quare fS 




9 feel 


= 


1 


(4 


yard, 




30J yards 


= 


1 


<< 


rod, pole, 


or perch, 


40 rods 


= 


1 


a 


rood, 




4 roods 


| 










10 square 


chains J 


1 


it 


acre, 




G40 a 


= 


1 


it 


mile. 




43.560 square feet are one acre. 








1G square perches 


1 


a 


chain. 




5 yards wide by 968 long 


contain one acre. 




10 " 


" " 484 " 


ti 


a 


tt 




20 " 


a a n±2 (I 


u 


a 


a 




40 " 


a a 221 " 


a 


t. 


a 




GO feet wide by 726 long contain 


one acre. 




110 " " 


" 39G " 


ti 


it 


a 




220 " 


" 198 " 


ti 


a 


ti 





the earth's motion. 57 

A strip of land one rod wide and one mile long is two 
acres. 

3 

1312 1311^- 
Measure 2504,,——, or — ^ *I J0 feet square, and vou have 
2o04 2504 ^ J 

one square acre. This last complex fraction is so nearly 
correct, that it makes a difference of only y-g-Q of one square 
inch in one hundred acres. 

A standard English mile is 5.280 feet in length, 1760 
yards, or 320 rods. 

A U. S. Government township comprises 36 sections, each 
a mile square. 

A section = 640 acres. 

A quarter section, half a mile square = 160 acres. 

An eighth section, half a mile long, north and south, and 
a quarter of a mile wide = 80 acres. 

A sixteenth section, a quarter of a mile square = 40 
acres. 

Among the ancients, Aristarchus, of Samoa, and Philo- 
laus, maintained that not only did our globe rotate on its 
own axis, but that it revolved around the sun in twelve 
months. Other astronomers taught the same doctrine. 
The Egyptians taught the revolution of Mercury around 
the sun, and others gave the same motion to Mars, Jupiter, 
and Saturn. 

The origin of the division of the Zodiac into constella- 
tions is lost in obscurity; though attributed to the Greeks, 
it has been ascertained to be of greater antiquity, possibly 
the Hindoos or Chinese. 

When on a railroad train making good time, say at the 
rate of forty miles an hour, fixed objects in view, such as 
houses, trees, fences, rocks, etc., are apparently hurrying 
past, while in reality we are hurrying past them; in like 
manner sun, moon, planets, and stars seem passing from 



58 THE sun's distance. 

east and west — this being in reality an apparent motion, 
because we are unconscious of our real motion of rapidly 
moving past them at the speed of over a thousand miles per 
hour. In this way we know that the earth revolves around 
the sun thousands of miles per hour in 

9. Sidereal year, 
lo\ Tropical or solar year, 
49.3 Anomalistic year. 
In our reckoning, we make every fourth year to contain 
366 days, and call it leap-year. Still greater accuracy re- 
quires, however, that the leap-day he dispensed with thi 
times in every 400 years. 

Whenever the number which denotes the year can be 
measured by 1, the year is leap-year, the centennial years 
excepted; and the centennial years divisible by 400 are also 
leap-years. The next centennial leap-year ifi 



D. 


ii. 


it 


365 


6 


9 


365 


5 


48 


365 


6 


13 



Calculation of the Distance of the Sun from the Earth. 

When the earth is in perihelion, or nearefet the sun, it 
then travels with its greatest velocity, and passes over an 
arc of 1° Or 9". 9 in a mean solar day. 

When the earth is in aphelion, or farthest from the sun, 
it passes over an arc in tin 4 same time of only 57' 11". 5. 

The earth in its circuit or revolution around the BUD 
sweeps over a distance of 580043925^^ mile-, at an av< 
speed or velocity of 18.38 miles per second, and mean dis- 
tance of 661G8 miles per hour, time and distance being the 
same and substituting a circle for the elliptic orbit. 

Hence the equation 
402.123859659493567 : 580043925.02 : : 128 : 18463371 6. The 
last term being the diameter, half of this, viz., 92316< s 



SOLAR YEAR. 59 

the radius of the orbit and the distance of the sun from 
the earth. This distance is from centre to centre, that is, dis- 
tance plus the radius of the sun and earth. Now, deducting 
half the diameter, or the radius of the sun and earth, 92316- 
858 — 432374 = 91.884484, we have the true and exact dis- 
tance of the earth from the sun, and thus this intricate prob- 
lem yields itself up to demonstration. 

91.884484 = Mean distance, 

93.425488 = Maximum 

90.343480 = Minimum 

The sun is a sphere, and is surrounded by an extensive 
and rare atmosphere. It is self-luminous, emitting light and 
heat, which art transmitted to a known distance of 2700 
millions of miles. 

The interval of time which intervenes from the moment 
when the sun leaves a fixed star until it returns to it again 
constitutes the sidereal year, and consists in solar time of 
365 d. 6 h. 9 m. 9 s.; therefore the sidereal year is longer than 
the mean solar year. The latter comprises the time between 
two successive passages of the sun through the same equinox. 
If the equinoxes were fixed points, then the period would be 
the same as the sidereal revolution ; but since these points are 
possessed of a retrograde motion from east to west of 50' 2" 
annually, and the sun returns to the equinox sooner every 
year by a period of time of 20 m. 23 s., the mean solar year 
is therefore 20 m. 23 s. shorter than the sidereal year, in con- 
sequence of the motions of the equinoctial points not being 
uniform. 

According to M. Delambre, if the earth be supposed to 
start from perihelion, it will require a longer interval of time 
than the sidereal period to reach perihelion again ; and the 
excess will be equal to the time necessary for the earth to 
describe IT 8" of its orbit; this it would do in 4m. 39.7s., 



60 sun's heat. 

which quantity must be added to the sidereal before we 
can ascertain the interval between two successive returns to 
perihelion. 

The result, then, is a period of 365.259581 mean solar 
days, which is called the anomalistic year. 

Multiply the earth's diameter (7925.555) by 108, and we 
have 855960, nearly the sun's diameter in miles. 

Multiply the sun's diameter (856.822, this diameter of 
the sun is calculated to correspond to my distance) by 108, 
and we have 92.536776, nearly the mean distance of the 
earth from the sun. 

Multiply the moon's diameter 2160 I by 108, and we have 
233280, nearly the mean distance of the moon from the 
earth. 

The proportion of the sun's heat that reaches 08 ifl only 
3J38ToVolToo- What the whole amount must be is beyond all 
human comprehension. Our annual share is sufficient to melt 
a layer of ice covering the surface of the earth to the depth 
of thirty-eight yards in thickness; and according to Pouell 
another calculation determines the direct light of the sun to 
be equal to that afforded by 6663 wax candles of modi rate 
size, supposed to be placed at a distance of one foot from the 
observer. The light of the moon being probably equal to 
that of only one candle at a distance of twelve feet, it follows 
that the light of the sun exceeds that of the moon 801072 
times, according to Wollasten ; Zollner's ratio is 61*000. 

The sun's mass, or attractive power, exceeds that of the 
earth 314.760 times. 

The tw T o points where the celestial equator intersects the 
elliptic are called the equinoxes (from ccquus, equal, and noz, a 
night), because, when the sun is at these points, day and night 
are theoretically equal. 

The points midway between these points are called the sol- 
stices (from sol, the sun, and stare, to stand still), because the 



kepler's discoveries. 61 

sun, when it has reached these neutral points, has obtained 
its greatest declination north or south, as the case may bej. 

Kepler's Discoveries. 

The square of Jupiter's period is to the square of Saturn's 
period as the cube of Jupiter's distance is to the cube of 
Saturn's distance. 

Kepler's first Law. — That all orbits are ellipses, with the 
sun or primary body in one of the foci of the ellipse. 

Second Law. — Equal areas of their orbits are described 
by the planets in equal times ; the orbit through its entire 
course is so balanced that the rapidity is exactly propor- 
tional to the nearness, and the slowness by the distance, in 
reference to each other ; so that equal areas of the orbit are 
described by the planets in equal times. 

Third Law. — That the squares of the periodic times of 
the planets are proportional to the cubes of their major 
axis or of their mean distances. (Seventy-eight years after 
Kepler's discoveries, Newton discovered the law of gravi- 
tation.) If, for. illustrating this Law, we take Mars and the 
Earth for an example, we find that the period of revolution 
of Mars is 686.23 days, and that of the Earth 365.6 days, 
and these periods, when squared, will give for the Earth 
8766 X 8766 = 76842756 hours, and for Mars 16487 x 
16487 = 271821169, and that the square of the period 
of Mars is therefore rather more than three times that of 
the earth. 

In like manner, if we take the mean distance of Mars, 
which is 140031954 millions of miles, and that of the 
Earth, which is 91.884484 millions of miles, we have in 
cubing these mean distances 140 X 140 X 140 = 2744000 
for Mars', and 91-^x 91 T % x 91 T 8 o = 773620 for the Earth's ; 
and dividing these results by each other, we shall find that 
6 



62 A DAY. 

the cube of the mean distance of Mars is rather more than 
three times the cube of the earth's mean distance. 

This proportion between the squares of the times and the 
cubes of the mean distances is found so universally to pre- 
vail with regard to all the planets and satellites, and other 
celestial bodies moving in orbits, that it has all the appear- 
ance of an absolute law. 



A Day. 

A day is either natural or artificial. A natural day is 
the space of time which elapses while the sun goes from any 
meridian until he arrives at the same again, or it fa the time 
contained from noon to noon, or the same hour again. 

An artificial day is the time between the sun's rising and 
setting, to which is opposed the night, the time the sun is 
hid under the horizon. 

All nations do not begin their day and reckon their hours 
alike. In most places in Europe the day is reckoned to 
begin at midnight, from whence is counted 12 hours till 
noon, then 12 more until next midnight, which make a 
day; yet astronomers commonly begin their day at noon, 
and reckon twenty-four hours until next noon. 

The Babylonians began their day at Bunrising, and r 
oned twenty-four hours until he rose again. This we call the 
Babylonish hours. 

The Jews and the Eomans divided the artificial days and 
nights into twelve equal parts. These were termed the Jewish 
hours, and were of different lengths, according to the seasons 
of the year — a Jewish hour in summer being longer than 
one in winter, and a night hour shorter, and the hours were 
styled the first, second, etc., of the day or night, so that 
midday always fell on the sixth hour of the day. These 



A MONTH. 63 

hours were also called planetary hours, because in every hour 
one of the seven planets was supposed to preside over the. 
world, and to take it by turns. The first hour after sun- 
rising on Sunday was allotted to the Sun, the next to Venus, 
the third to Mercury, and the rest in order to the Moon, 
Saturn, Jupiter, and Mars. By this means, on the first hour 
of the next day the Moon presided, and so gave the name 
to that day; and so the seven days, by this method, had 
names given them from the planets that were supposed to 
govern on the first hour. 

All nations that have any notion of religion set apart 
one day in seven for public worship. The day solemnized 
by Christians is Sunday, or the first day of the week, being 
that on which our Saviour rose from the grave, and on which 
the apostles afterwards used more particularly to assemble 
together to perform divine worship. 

The Jews observed Saturday, or the seventh day of the 
week, for their Sabbath or day of rest, being that appointed 
in the fourth commandment under the law. The Turks per- 
form their religious ceremonies on Friday. 



A Month. 

A month is that space of time measured by the moon in 
its course around the earth. A lunar month is periodical' 
or synodical. A periodical is that space of time the moon 
takes to perform her course from one point of the elliptic 
till she arrives at the same again, which is 27 days and some 
odd hours ; and a synodical month is the time between one 
new moon and the next, about 29i days. But a civil month 
is different from these, and consists of a number, according 
to the laws and customs of the country wherein they are 
observed. 



64 A YEAR. 



A Year. 



The civil year is the same with the political established 
by the laws of a country, and is either movable or immov- 
able; the movable year consists of 365 days, being less than 
the tropical, and is called the Egyptian year, because ob- 
served in that country. 

The Romans divided the year into twelve calendar months, 
to which they gave particular names, that are still retained 
by most nations. 

The year is also divided into four quarters or 
Spring, Summer, Autumn, and Winter. These quarters are 
properly made when the sun enters into the equinoctial and 
solstitial points of the elliptic; but in civil uses they are differ- 
ently reckoned, according to the customs of the several coun- 
tries. In the United States and England we commonly reckon 
the first day of January to be the first in the year, which is 
commonly called New-Year's Day. In ecclesiastical aflaira 
the day is reckoned to commence on Lady-Day, which is the 
25th March, and from thence to midsummer day, which ifl 
the 24th June, is reckoned the first quarter; from midsum- 
mer day to Michaelmas-Day, which is the 29th of September, 
is the second quarter; the third quarter is reckoned from 
Michaelmas-Day to Christmas-Day, which is the 25th of I 
cember, and from Christmas-Day to Lady-Day is reckon 
the last quarter in the year. In common affairs, a quarter 
is reckoned from a certain day to the fourth month follow- 
ing; sometimes a month is reckoned four weeks or 28 da 
and so a quarter 12 weeks. To all the inhabitants in the 
1 southe™} hemispheres, their midsummer is properly when the 
sun is in the tropics of 'fcapriSSn] and their midwinter at the 
opposite time of the year; but those who live under the 
equinoctial have two winters, viz., when the sun is in either 



A YEAR. 65 

tropic ; although properly there is no season that may be 
called winter in those parts of the world. 

The Egyptian year of 365 days being less than the true 
solar year by almost six hours, it follows that four such years 
are less than four solar years by a whole day, and therefore 
in 365 times four years, that is in 1460 years, the beginning 
of the year moves through all seasons. To remedy this in- 
convenience, Julius Csesar (considering that the six hours 
that remain at the end of every year will in four years 
make a natural day) ordered that every fourth year should 
have an intercalary day, which therefore consists of 366 days. 
The day added was put in the month of February by post- 
poning St. Matthias's day, which in common years falls on 
the 24th, to the 25th of said month ; all the fixed feasts in 
the year from thenceforward falling a week-day later than 
they would otherwise. 

According to the Roman way of reckoning, the 24th of 
February was the sixth of the Calends of March ; and it 
was ordered that for this year there should be two sixths, or 
that the sixth of the Calends of March should be twice 
repeated, upon which account the year was called Bissextile, 
which we now call the leap-year. To find whether the year 
of our Lord be leap-year, or the first, second, or third after, 
divide it by four, and the remainder, if any, shows how many 
years it is after leap-year ; but if there be no remainder, then 
that year is leap-year. 

This method of reckoning the year, making the common 
year to consist of 365 days, and every fourth year to have 
366 days, is called the Julian account, or the old style. 

But the time appointed by Julius Csesar for the length 
of a solar year was too much. At the time of the Council of 
Nice (where the terms were settled for observing Easter), 
the vernal equinox fell upon the 21st of March ; but by 
its falling backwards 11 minutes every year, it was found 
6* E 



66 THE STARS. 

that in A. D. 1582, when the calendar was corrected, the 
sun entered the equinoctial' circle on the 11th of March, 
having departed ten whole days from its former place in 
the year. Pope Gregory XIII., therefore, designing to 
place the equinoxes in their former situation with re 
to the year, took these ten days out of the calendar, and 
ordered that the 11th of March should be reckoned as the 
21st. To prevent the of the year from going back- 

wards for the future, he ordered thai every hundredth year, 
which in the Julian form was to ho a Bissextile, should 
be a common year, and consist only of 365 days; but that 
being too much, every fourth hundred was to remain Bi 
tile. This form of reckoning, being established by the au- 
thority of Pope Gregory XI IT., is called the I ian ac- 
count, or the new style, and i.- observed in all Christian 
countries. 

In the year 1752, when the Gregorian calendar was 
adopted by the English government, eleven days had to be 
dropped out of the almanac Even the ( 
does not give exactly correct results, but by a slight change 
can be so adjusted that it will not vary the commencement 
of the year more than a day in one hundred thousand ; 



The Stars. 

The fixed stars arc those bright and shining bodies which 
on a clear night appear to us everywhere dispersed tin 
the boundless regions of space. They are termed fixed be- 
cause they have been found to keep the same immutable 
distance one from another in all ages, without having any of 
the motions observed in the planets. The fixed stars are all 
placed at such immense distances from us that the best of 
telescopes represent them no larger than points, without 
having any diameters. 



THE STARS. 67 

It is evident that all the stars are luminous bodies, and 
shine with their own proper and native light, else they could 
not be seen at such a great distance. For the satellites of 
Jupiter and Saturn, although they appear under considerable 
angles through good telescopes, are altogether invisible to 
the naked eye. The distance between us and the sun is 
vastly large when compared to the diameter of the earth ; 
yet it is nothing, when compared with the enormous distance 
of the fixed stars, for the whole diameter of the earth's an- 
nual orbit appears from the nearest fixed stars no larger 
than a point, and the fixed stars are at least 100000 times 
farther from us than we are from the sun. 

Hence it follows that though we approach nearer to some 
fixed stars at one time of the year than we do at the oppo- 
site period, and that by the whole length of the diameter 
of the earth's orbit; yet this distance being so small in com- 
parison with the distance of the fixed stars, their magnitudes 
or positions cannot thereby be sensibly altered; therefore 
we may always, without error, suppose ourselves to be in 
the same centre of the heavens, since we always have the 
same visible prospect of the stars without any alteration. 

If a spectator were placed as near to any fixed star as we 
are to the sun, he would then observe a body as large, and 
every way like, as the sun appears to us, and our sun would 
appear to him no larger than a fixed star ; and undoubtedly 
he would reckon the sun as one of them in numbering the 
stars ; therefore, since the sun differs nothing from a fixed 
star, the fixed stars may be reckoned as so many suns. 

It is not reasonable to suppose that all the fixed stars are 
placed at the same distance from us; but it is more probable 
that they are everywhere interspersed through the vast in- 
definite space of the universe, and that there may be as 
great a distance between any two of them as there is be- 
tween our sun and the nearest fixed star. 



68 THE STARS. 

Hence it follows why they appear to us of different mag- 
nitudes, not because they are at different distances from 
us, those that are nearest excelling in brightness and lus- 
tre, those that are more remote, which give a fainter light, 
and appear smaller to the eye. 

Astronomers distribute the stars into several orders or 
classes, — those that are nearest to us, and appear brightest to 
the eye, are called stars of the first magnitude; those that 
are next in brightness and lustre are called stars of the 
second magnitude ; those next the third, and so continued 
to stars of the sixth magnitude, which are the smallest that 
can be discovered by the naked eye. There are infinite 
numbers of smaller stars that can be Been through telesco] 
but these are not reduced to any of the six orders, being 
called telescopical stars. 

The ancient astronomers, that they might distinguish the 
stars in regard to their situation and position to each other, 
divided the whole starry firmament into several asterisms, 
or systems of stars, consisting of those that are near to one 
another. These asterisms are called constellations, and are 
fancifully compared with the forms of some animals, as men, 
lions, bears, serpents etc., or to the imaj some known 

things, as of a crown, a harp, a triangle, etc. 

The starry firmament was divided by the ancients into 48 
images or constellations, twelve of which they placed in that 
part of the heavens wherein are the planes of the planetary 
orbits, which part is called the Zodiac, because most of the 
constellations placed therein were supposed to resemble some 
living creature. The two regions of the heavens that are on 
each side of the Zodiac are called the north and south parts 
of the heavens. The ancients placed these particular constel- 
lations or figures in the heavens either to commemorate the 
deeds of some great man or of some notable exploit or 
action, or else took them from the fables of their religion ; 



THE STARS. 69 

and the modern astronomers still retain them, to avoid 
the confusion that would arise by making new ones when 
they compared the modern observations with the old ones. 
Some of the principal stars have particular names given 
them, as # Sirius, Arcturus, etc. 

There are also several stars that are not reduced into con- 
stellations, and these are called unformed stars. 

Besides the stars visible to the naked eye, there is a very 
remarkable space in the heavens called the galaxy, or milky 
way. This is a broad circle, of a whitish hue like milk, going 
quite round the heavens, and consisting of an infinite number 
of small stars, visible through a telescope, though not dis- 
cernible to the naked eye by reason of their exceeding faint- 
ness; yet with their light they combine to illustrate that part 
of the heavens where they are, and to cause that shining 
whiteness. 

The places of the fixed stars, or their relative situation one 
to another, have been carefully observed by astronomers and 
collected in catalogues. 

The first among the Greeks who reduced the stars into a 
catalogue was Hipparcus, who, from his own observations 
and of those who lived before him, inserted 1022 stars upon 
his catalogue, about 120 years before the Christian era. 
This has been increased to about three thousand discern- 
ible by the naked eye. 

It may seem strange to some persons that there are no 
more than this number of stars visible to the naked eye, for 
sometimes on a clear night they appear to be innumerable ; 
but this is only a deception of our sight, arising from their 
constant sparkling, while we look upon them confusedly, 
without reducing them into any order, for there can sel- 
dom be seen above 1000 stars in the whole heavens, with the 
naked eye, at the same time; and if we distinctly view them, 



70 THE STARS. 

we will not find one but what is marked upon a good celes- 
tial globe. 

Although the number of stars that can be discerned by 
the naked eye are so few, yet there are many more which 
are beyond the reach of our vision. Through telescopes they 
appear in vast multitudes dispersed throughout the firma- 
ment, and the better the glasses the more appear. 

Those who think that all of these glorious bodies were 
created for no other purpose than to impart to us a little 
dim light must entertain a very weak idea of the Divine 
Wisdom. We receive more light from the moon itself, be- 
cause of its comparative nearness, than from all the stars 
put together. Nevertheless, this comparison does not in the 
least detract from the actual resplendent character or reality, 
no, not one iota. 

The firmament is a creation of the Almighty and his 
diadem or crown of glory, the sparkling stars the jewels 
thereof. Seeing that the planets are subject to the same laws 
of motion with our earth, and some of them are not only equal, 
but vastly exceed it in magnitude, it is not unreasonable to 
suppose that they are all inhabitable worlds. And since the 
fixed stars are no way behind our sun, either in size or lus- 
tre, is it not probable that some, if not all of them, have a 
system of planetary worlds turning around them as we do 
around our sun ; and if we ascend as far as the smallest star 
we can see, shall we not then discern innumerably more of 
these glorious bodies which now are altogether invisible to 
us, and so ad infinitum through the boundless space of the 
universe ? 

What a magnificent idea must this raise in us of the 
Divine Being ! who is everywhere and at all times present, 
displaying his power, wisdom, and goodness amongst all 
his creatures ! 



TABLE OF DEGREES OF LONGITUDE. 71 

Length of a Degree of Longitude in Different Latitudes 
and at the Level of the Sea. 

These lengths are in common land or statute miles of 
5280 feet. Since the figure of the earth has never been 
precisely ascertained, these are but close approximations. 





1 


P O 


o 
1 


Pi © 


1 


P C 


1 





69.17 


22 


64.18 


44 


49.83 


64 


30.38 


2 


69.13 


24 


63.29 


46 


48.13 


66 


28.22 


4 


69.00 


26 


62.22 


48 


46.31 


68 


25.98 


6 


68.80 


28 


61.12 


50 


44,54 


70 


23.73 


8 


68,50 


30 


59.93 


52 


42.66 


72 


21.44 


10 


68.13 


32 


58.68 


54 


40.73 


74 


19.13 


12 


67.67 


34 


57.39 


56 


38.74 


76 


16.80 


14 


67.13 


36 


56.00 


58 


36.70 


78 


14.45 


16 


66,50 


38 


54,57 


60 


30.64 


80 


12.08 


18 


65.80 


40 


53.06 


62 


32,53 


82 


9.69 


20 


65.04 


42 


51.47 











Limits of Vegetation in the Temperate Zones. 
The vine ceases to grow at about 2300 feet above the level 
of the sea ; Indian corn, at 2800 ; oak, at 3350 ; walnut, at 
3600 ; ash, at 4800 ; yellow pine, at 6200 ; and fir, at 6700. 

Perpetual snow under the equator at 15800 feet above 
the level of the sea ; in latitude 45°, at 8400 ; and in lati- 
tude 65°, at 5000. 



Equation of Payments. 

Kule 1. — Multiply each debt by the number of days, 
counting from the time of the earliest date to the date of 
each sum respectively ; then divide the sum of these prod- 
ucts by the sum of the account : the quotient will give the 



72' EQUATION OF PAYMENTS. 

number of. days to count, from the first debt, for the average 
date of the account. 

Note. — Since the first debt is the period from which the average 
time is computed, it must be left out of the dividend, but must be in- 
cluded in the divisor. 

Rule for unequal credits, viz., for six, nine, and twelve 
months. — Find the date when due, and apply the rule 
above, which will give the average date when due. 

Eule 2. — Take the difference of time between each pay- 
ment and the last, which arrange and multiply as in exam- 
ple below; then divide the sum of this product by the 
whole amount, and the quotient will be the number of (L 
to count back from the last, date in the arrangement 









Bams. l Pro 


First amount fell due 


February 19 


900 x 185= 166500 


Second " 


a 


March 1, 


4,000 x 175= TonouO 


Third " 


a 


March 3, 


3,500 x 17:;.- : on 


Fourth " 


tc 


March 6, 


8,640 x 170- =146i 


Fifth 


u 


March 18, 


6,300 x 158= 005400 


Sixth 


a 


April 29, 


5,000 x 110— 580000 


Seventh " 


a 


August 23, 


500 x 1= 500 



M0 )4516700 

Quotient, 157 days nearly. 

So the $28,840 fall due on March 19th, counting back 
157 days from August 23d. 



Explanation of the table of days showing the number of 
days from any date in one month to the same date in any 
other month. 

Example. — How many days from September 9th to 
March 9th? Look for Sept. at the left hand, and March 
at the top — in the angle is 181. In leap-year, add one day 
if February is included. 



INTEREST. 



73 



Table of Days for Interest, etc. 



FROM 


To 
Jan. 


To 
Feb. 


To 

Mar. 


To 

Apr. 


To 
May. 


To 

June 

151 
120 


To 
July 

181 

150 


To 
Aug. 

212 

181 


To 

Sept. 

243 
212 


To 

Oct, 

273 
242 


To 

Nov. 

304 

273 


To 
Dec. 

334 

303 


January.... 


365 


31 


59 


90 


120 

89 


February .. 


334 


365 


28 


59 


March 


306 


337 


365 


31 


6± 


92 


122 
91 


153 

122 


184 
153 


214 
183 


245 
214 


275 
244 


April 


275 


30G 


334 




30 


61 


May 


245 
214 


276 
245 


304 
273 


335 

304 


365 
334 


31 
365 


61 
30. 


92 
61 


123 
92 


153 
122 


184 
153 
123 


214 

183 

153 

122 

91 

61 

30 

365 


June 


July 


184 


215 


243 


274 


304 


335 


365 


31 


62 


92 


August 


153 


184 


212 


243 


273 


304 


334 
303 
273 


365 
334 
304 


31 
365 
335 


61 

30 

365 

334 

304 


92 

61 

31 

365 

335 


September 


122 


153 


181 


212 242 


273 
243 


October.... 


92 


123 


151 


182 212 


November 


61 


92 


120 


1511181 


212 


242 


273 


304 
274 


December. 


31 


62 


90 


121 1 151 


182 


212 


243 



Table of Experiments made by the British Admiralty with 

Wire and Hempen Rope and Chain— Comparative 

Strength. 



Circumference Circumference 

of of 

Wire Rope. [ Hempeu Rope. 


Diameter of 
Chain. 


Breaking 
Weight. 


Inches. 
2 
3 
4 


Inches. 

5 

8 

10 


Inches. 

l 

2" 
13 
T6 
31 
32 


Lbs. 
14,224 
26,880 
43,232 



74 INTEREST. 

Explanation of the Following Interest Table. 

The principal, beginning at 1 dollar and progressing to 
2000, is to be found at the top of the page ; the time in the 
left hand margin of each page begins at the top with 1 
day, proceeding down in regular order to 30 days, and alter 
the blank line the months begin and proceed in like man- 
ner, so that we have in view on the same page the in i 
of the sum required for years, months, and days; if the in- 
terest is required for two years, double the year. 

Example. — Required the interest for 2 years, 9 months, 
17 days on 50 dollars. Turn to 50, at the top of column, 
page 79, and you have at the bottom, 

in line with 12 mos., $3.00 X 2 = $6.00 

" " " 9 mos. 2.25 

" " " 17 days .14 

These added together is the interest required, $8.39 

If we want the interest on part of a dollar, turn to the 
cent table on page 8G. 

If 1 per cent, ib required, divide t<'>VJ by six. 

If 2 per cent, is required, divide by three. 

If 4 per cent, is required, deduct one-third. 

If 5 per cent, is required, deduct one-sixth. 

If 7 per cent, is required, add one-sixth. 

If 8 per cent, is required, add one-third to the above. 

If 9 per cent, is required, add one-half. 

If 10 per cent is required, add two-thirds. 

If 11 per cent is required, add five-sixths. 

If 12 per cent is required, multiply by two. 



•INTEREST TABLE. 



75 



Interest Table at 6 Per Cent. 



Days. 


DOLLARS. 


1 


2 


3 


4 


5 


6 7 8 


9 


10 


11 


1 





o 




















1 


2 




















o 








3 














o 

















4 























1 


1 


1 


5 




















1 


1 


1 


1 


6 

7 











o 







1 1 


1 


1 


1 

















111 


1 


1 




8 











° 




1 1 1 


1 


1 


1 


9 
10 
11 


o 













111 


1 


1 


2 



















1 


1 


2 


2 


o 















.2 


2 


2 


2 


12 


o 





1 








1 


2 


2 


2 


13 


o 





1 








2 2 


2 


2 


2 


14 
15 








1 








2 1 2 


2 


2 


2 








1 








2 j 2 


2 


2 


2 


16 








1 1 






2 2 


2 


3 


3 


17 
18 

19 
20 
21 
22 
23 
24 





1 1 




2 


2 2 


3 


3 


3 








1 1 




2 


'2 2 


3 


3 








1 






2 


2 i 3 


3 


3 


3 






o 




1 








2 || 3 


3 




4 


1 




2 


2 


2 3 


3 


4 


4 





1 






2 


2 


3 3 


3 


4 


4 


o 


2 


2 3 J 3 


3 


4 


4 







1 


2 


2 


2 3 3 


3 


4 


4 


23 
26 
27 

"28 

29 

30 

Mos. 

1 

2 









2 


2 


2 3 3 


4 


4 


5 









2 


2 


3 3 3 


4 


4 


5 









2 


2 


3 3 4 


4 


5 


5 









2 


2 


3 3 4 


4 


5 


5 









2 


2 


3 ; 3 4 


4 


5 


5 









2 


2 


3 ! 3 4 


4 


5 


5 






1 


! 


1 


1 


2 


2 


3 3 4 


4 


5 


5 


1 


2 


3 


4 


5 


6 7 


8 


9 


10 


11 


3 
4 


1 


3 


4 


6 


7 


9 | 10 


12 


13 


15 


16 


2 


4 


6 


8 


10 


12 14 


16 


18 


20 


22 


5 


o 


5 


7 


10 


12 


15 17 


20 


22 


25 


27 


6 


3 


6 


9 


12 


15 


18 ! 21 


24 


27 


30 


33 


7 


3 


7 


10. 


14 


17 


21 24 


28 


31 


35 


38 


8 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


9 


4 


9 


13 


18 


22 


27 


31 


36 


40 


45 


49 


10 


5 


10 


15 


20 


25 


30 


35 


40 


45 


50 


55 


11 
12 


5^ 


11 


16 


22 


27 


33 


38 


44 


49 


55 


6-0 


12 


18 


24 


30 


36 42 


48 


54 


60 


66 



76 



INTEREST TABLE. 



Interest Table at 6 Per Cent— Continued. 



Days, 

1 
2 
:i 
l 
5 


DOLLARS. 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 
































'I 













1 


i 


i 


i 


i 


i 


1 


1 


1 


1 




1 


i 


i 


i 


i 


i 


1 


1 


1 


1 




1 


i 


i 


i 


i 


i 


1 


1 


1 


1 




1 


i 


i 


i 


•j 


9 







1 


1 


1 




2 




2 


•i 


•j 




2 


7 
8 


1 


1 


2 


2 


2 


2 




2 




2 




•1 


■1 


•J 


2 


■1 


2 


2 


■1 








9 
10 

11 

12 

ia 

n 

15 
16 
17 
is 
19 
20 
21 
22 
2:* 

21 
2.1 
26 

27 
28 
29 
SO 

Mos. 
1 
2 


■1 
■1 


2 


2 


•1 


•J 


B 


8 


8 








2 


2 


■1 


8 


8 










1 


■1 
3 

3 


2 
3 
3 

3 


3 


8 










4 


1 


4 


8 


8 




i 


I 


l 


l 


1 


:; 


1 


1 


1 


•1 


4 




3 


1 


I 


4 


1 


6 






:; 


8 




1 


1 


l 










:; 




1 


1 


1 


1 


5 










8 


\ 


I 


1 


4 


5 




5 






6 


1 


1 


I 


5 


:» 






6 


6 




7 


I 


1 


1 


6 


5 




6 




6 


7 


7 


4 


4 


5 


•"» 


•". 




6 


6 


7 


7 




1 


6 




5 


6 


6 




7 


7 


7 




1 


5 








6 


6 


7 


7 








5 


5 


6 


6 


7 


7 


7 


8 






5 


5 


6 




6 


7 


7 


7 




8 




5 


5 


6 


6 


7 


7 








9 


LO 


5 


6 


6 


7 


7 
7 


7 


- 




9 


9 


6 


6 




7 


B 






LO 
LO 


10 

10 

11 


6 


6 


7 


7 


B 


8 
8 


9 


9 
9 


10 
LO 


6 


6 


7 


7 




6 


6 


7 


7 




LO 


11 
























6 


6 


7 


7 




8 


L8 
27 


9 

VJ 


10 


LO 

•Jl 
81 


11 
44 

77 


L2 


L3 


14 


15 


16 
24 


17 
25 
34 


:i 


is 


20 


21 


23 






4 


24 


26 


28 










5 


30 


32 


35 


37 


40 

L8 


51 


L5 

54 


17 
57 




6 

7 


36 


39 


12 




42 
48 


45 
52 


19 
56 


60 


64 


59 


8 

9 

10 

11 

12 


72 


76 








54 






67 


72 




M 








60 
66 


65 

71 


70 
77 


75 
82 


88 


93 


HIS 


96 

HI 
111 


no 
120 


115 
126 


lid 
1J1 


72 


78 


84 


90 


96 


L02 



INTEREST TABLE. 



77 



Interest Table at 6 Per Cent. — Continued. 



Days. 


DOLLARS. 


23 24 


25 


26 


27 


28 


29 30 


31 


32 


33 


1 





o 











| 


i 


i 


i 


2 


i i 


i 


i 


i 


i 


i i 


i 


i 


i 


i 


1 


i 


i 


i 


i 


l ; l 


2 


2 


2 


4 


2 


2 


2 


2 




2 


2 


2 


2 


2 


2 


5 

6 




2 


2 


2 


2 


2 


2 


2 


3 


3 


3 


2 
3 


2 


2 


3 


3 


3 


3 


3 


3 


3 


3 


7 


3 


3 


3 


3 


3 


3 




4 


4 


4 


8 


3 


3 




3 


4 


4 


4 


4 


4 


4 


4 


9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 

2a 

24 

25 
2t> 
27 

28 
29 


3 


4 


4 


4 

4 


4 


4 


4 


4 


5 


5 


5 


4 


4 


4 


4 


5 


5 


5 




5 


5 


4 


4 


5 


5 


5 




5 


5 


6 


6 


6 


5 


5 


5 


5 


5 


6 




6 


6 


6 


7 


5 


5 


5 




6 




6 


6 


7 


7 


7 


5 


6 


6 


6 


6 


6 


7 


7 


7 


7 


8 


6 


6 


6 


6 


7 


7 


7 


7 


' 8 


8 


8 


6 


6 


7 


7 


7 


7 


8 




- 


^ 


9 


6 


7 


7 


7 


8 


- 


- 


8 




9 


9 


7 


7 


7 


8 


8 


8 


9 


9 


9 


9 


1" 


7 


7 


8 


8 


8 


g 


9 




10 


10 


I'- 


8 


8 


8 


9 


9 




LO 




10 


11 


ll 


8 


8 


9 


9 


9 


10 


10 10 


11 


11 


12 


8 
9 


9 


9 


10 


10 


10 


11 


11 


11 


11 


12 


9 


10 


10 


10 


11 


11 


11 
12 


12 


12 


13 


9 


10 


10 


10 


11 


11 


12 


12 


13 


13 


1Q 


10 


10 


11 


11 


12 


12 


12 
13 


13 


13 


14 


10 


ID 


11 


11 


12 


12 


13 


13 


14 


14 


10 


11 


11 


12 


12 


13 


13 


14 


14 


14 


15 


11 


11 


12 


12 


13 


13 


14 


14 


15 


15 


15 


11 


12 


12 


13 


13 


14 


It 


14 


15 


15 


16 


30 

Mos. 

l 

2 
3 


11 


12 


12 


13 


13 


14 


14 


15 


15 


16 


16 
























11 


12 


12 


13 


13 


14 


14 


15 


15 


16 


16 


23 


24 


25 


26 


27 


28 


29 


30 


31 


32 


33 


34 


36 


37 


39 


41 
54 

68 


42 


44 


45 


47 


48 


50 


4 


46 


48 


50 


52 
65 


56 


58 


60 


62 


64 


66 


5 


57 
69 


60 


62 


70 


73 


75 


78 


80 


83 
99 


6 

7 


72 


75 


78 


81 


84 


87 


90 
105 


93 


96 


80 


84 


S7 
100 


91 


95 


98 


102 


109 
124 


112 

128 


116 

132" 


8 

9 

10 

11 

12 


92 
103 
115 
126 

~138~ 


96 


104 


108 


112 


116 


120 


108 
120 " 
132 
144 


112 
125 

137 
150 


117 
130' 
143 
156 


122 
135 
149 


126 
140 

154 


131 
145 


135 
150 


140 


144 


149 


155 


160 


165 


160 


165 


171 


176 


182 


162 


168 


174 


180 


186 


192 


198 



78 



INTEREST TABLE. 



Interest Table at 6 Per Cent— Continued. 



Days, 

_____ 

2 


DOLLARS. 


34 


35 


36 


37 


38 39 


40 


41 


42 


43 


44 

i 


l 


i 


1 


i 


i 


1 


i 


i 


i 


i 


1 


i 


1 


i 


i 


1 


i 


i 


i 


i 


i 

2 
1 


:* 
1 
5 
6 


2 


2 


2 


2 


2 


2 


2 

:; 


2 


2 

8 

o 


2 
1 


2 
3 
3~ 


2 


2 


2 


2 


8 


3 ' 

:; 
1 


8 


S 


;; 


8 


8 


8 


1 


1 


1 


i 


i 


l 


i 


4 




7 
8 


4 


4 


I 


1 


i 












1 
5 


5 


6 


6 

7 
7 

9 
LO 
LO 

11 


o 


5 

o 




6 


o 


7 
7 


i) 
10 
11 
12 
13 
11 
IS 
16 
17 
IS 
1<> 
20 
21 
22 
2:; 

21 
20 

2<; 

27 
2S 
29 
150 

Mos. 

l 


5 


6 

7 
7 

9 


7 


7 


6 

7 


7 


6 
6 


6 
6 


7 
7 

9 
9 
10 

11 
11 

12 

L3 

l:; 
U 

15 
15 

L6 
L6 

17 

L8 

10 


7 


7 


7 








7 


7 
7 







7 




1<> 
in 
11 


9 


9 






10 

11 
11 
12 
10 
11 
U 
15 


in 

10 

11 
12 

12 

18 

11 

15 
10 

17 
18 
18 

10 


8 

B 


9 
9 


w 


10 


10 

11 
11 

12 
10 

L8 

11 

10 


9 


9 
LO 


11 
11 


11 

12 


10 

LO 

11 
11 
[2 


LO 


LO 


U 


12 
12 
l:: 
11 
11 
15 

10 


12 

10 
10, 

11 
i:. 

10 


12 

13 

11 
11 


11 
12 
12 


11 
L2 
18 


L2 
12 

1 I'- 
ll 
11 

15 

L5 

10 
17 
17 
L8 
L8 


12 
18 

11 
u 
15 
L5 
16 
16 
17 


13 
18 

U 
15 

i:> 
[6 
16 

17 
17 


L3 
14 
14 

15 

L6 
16 

17 
17 
18 


10 

16 


15 

L6 

17 
17 

is 


10 
10 
17 
L8 

10 


1.-, 

17 
17 
18 

10 

0.. 


L6 

17 
18 
L8 

10 


L6 

17 
L8 
L8 

10 
10 


10 


10 


20 

21 


21 
21 


21 
21 
22 


2<i 


17 
34 






















17 
35 


18 
36 


87 


19 
57 


10 


2<i 
0" 


41 
62 
B2 

or, 


21 
12 

0, 


21 

o; 


11 


2 


3 


51 
68 




54 


56 






4 


7h 


72 


71 


76 


78 


5 


B5 


88 


90 


00 
Ill 


95 

111 




100 




lln 


6 


1(112 


105 


L08 


117 


L20 


128 


117 


129 

101 


154 


7 
8 


111) 
136 


123 
140 


126 


130 


133 


107 


110 


141 


144 


lis 


L52 


100 


160 


104 


172 


176 


9 


153 


158 


162 


107 


171 


170 


180 


185 




101 




10 


170 


175 


180 


185 


190 


195 


200 




210 


210 




11 
12 


187 


193 


198 


204 


209 


210 


220 








212 


204 


210 


216 


222 


22S 


20.4 


240 


246 


252 





INTEREST TABLE. 



79 



Interest Table at 6 Per Cent. — Continued. 



Days. 


DOLLARS. 


45 


46 


47 48 


49 


50 


51 52 53 54 55 


1 


l 


1 


1 


1 


i 


i 


1 ! 1 


1 


1 


1 


2 


1 


2 


2 


2 


2 


2 


2 


2 


2 


2 


2 


3 
4 


2 
3 


2 
3 


2 


2 


2 


2 


3 


3 


3 


3 


3 


3 


3 


3 


3 


3 


3 


3 


4 


4 


5 


1 


4 


4 


4 


4 


4 


4 


4 


4 


4 


4 


6 


4 


5 


5 


5 


5 


5 


5 


5 


5 


5 


5 


7 
8 


5 
6 


5 


5 


6 


6 


6 


6 


6 


6 


6 


6 


6 


6 


6 


6 


7 


7 


7 


7 


7 


7 


9 


7 


7 


7 


7 


7 


7 


8 


8 


8 


8 


• 8 


10 


7 


8 


3 


8 






8 


9 


9 


9 


9 


11 


8 

~ 10 
11 
11 
12 
13 
1~3 


8 


8 
9 
10 
11 
12 
12 
13 




9 


'J 


9 




10 




10 


12 


9 
10 

11 
12 
12 
13 


9 
10 


10 


10 


10 


10 


10 


11 




13 
14 
15 
16 
17 
IS 
19 
20 
SI 
22 
2:5 
24 


10 


11 


11 


11 


11 


12 


12 


11 
12 
13 
14 


11 
12 
13 

11 
11 


12 
12 
13 

11 


12 
13 
13 
14 


12 
13 
14 

15 
15 


12 
13 

14 
15 
16 


12 
13 
14 
15 


14 
11 

15 


11 


14 


14 


15 


15 


17 
18 


18 


11 


15 


15 


15 


15 


16 


16 


16 


17 


15 
16 
16 


15 

16 

17 


16 


16 


16 




17 


17 


17 


16 
17 


17 
18 


17 
18 


18 

18 


18 


18 


19 


19 

20 


19 


19 


ID 


17 


18 


18 


18 


19 


l'.i 
20 


~*20 


20 
21 


20 


21 




18 


18 


19 


19 


2n 


21 




22 


2> 
26 


19 


19 


20 


20 


_ 


21 

22 


21 
22 




22 

_ 


23 


20 


20 


20 • 


21 


21 


27 


20 


21 


21 


22 


22 


22 


23 


23 


24 


24 


25 


28 
29 
30 
Mos. 
1 


21 


21 


22 


22 


23 




24 


24 


25 


25 




22 


22 


23 


23 


24 


24 


25 




26 


26 


27 


22 


23 


23 


24 


24 


25 


25 


26 


26 


27 


27 






















• 


22 


23 


23 


24 


24 


25 


25 


26 


26 


27 


27 


2 


45 


46 


47 


48 


49 


50 


51 


52 


53 


54 


55 


3 


68 
90 


69 


71 


72 


74 


75 


77 


78 


80 


81 


83 


A 


92 


94 


96 


98 


100 


102 


104 


106 


108 


110 


5 


113 


115 


118 


120 


123 


125 


128 


130 


133 135 


138 


6 


135 


138 


141 


144 


147 


150 


153 


156 


159 162 105 


7 


158 
180 
203 


161 


165 


168 


172 


175 


179 


1S2 


186 


189 193 


8 


184 


188 


192 


196 


200 


204 


208 


212 


216 220 


9 


207 


212 


216 


221 


225 


230 


234 


239 


243 ; 248 


10 


225 


230 


235 


240 


245 


250 


255 


260 


265 


270 1 275 


11 


248 


253 


259 


264 


270 275 


281 


286 


292 


297 


303 


12 


270 


276 , 282 


288 294 300 306 312 318 


324 


330 



80 



INTEREST TABLE. 



Interest Table at 6 Per Cent— Continued. 



Days. 

1 

2 

:* 

I 

r> 

6 

7 

S 

9 
10 
11 

12 
18 
11 
10 
16 

17 
is 
19 
20 
21 
22 
23 
2 1 
25 
26 
27 
2S 
20 

:*o 

Mos, 

1 


E> O I, LA II S. 


56 


57 


58 


59 


60 


61 


62 


63 


64 

1 
2 


65 


66 

1 


1 


1 


1 


1 


1 


1 


1 


1 
2 


1 
2 


2 


2 


2 

3 


2 

1 


2 
1 


2 


2 


:; 


3 












1 


1 


1 


1 


1 


1 


1 

7 


1 




6 


5 


5 




5 




6 


7 


6 

7 








7 


6 

7 

9 
10 

11 
12 
13 


7 
7 

9 
10 
11 
L2 
13 


7 


7 7 7 


7 


3 
11 




- 


- 






- 


- 


LO 
LO 

11 
L2 

1:; 


10 

11 
L2 

l:; 


9 

10 


LO 


LO 

11 
L2 

1:; 


LO 


11 


11 


11 

12 

l:; 


11 
12 

1 • 


11 

12 
13 


12 


L2 
L3 
M 


L2 

11 


11 




11 


11 


11 


16 
L6 
17 
18 


L6 
18 


16 

17 

-1 


11 


U 


11 
>' 
16 

17 


15 

1.; 

17 


17 
is 


1 i 
1.; 

17 
18 


1.. 




L5 

in 

17 
17 


1:. 
16 

17 


1.; 

17 
18 


L8 




L9 
21 




L8 


19 

22 
24 

27 


L8 

l'.i 


10 


19 


P.. 


is 

•J<) 
21 

24 
26 


L9 

•jo 

21 

22 

24 

26 
27 


21 


21 


24 
27 


21 
27 




















31 


31 




;:i 




27 
28 






29 














28 

56 
84 
112 

lit) 


.".7 
86 

HI 

1 !:; 


28 

87 

in; 
ii:> 


lis 


90 


61 


62 
124 


:;i 


64 




2 


128 




4 




5 


214 
244 


6 

7 
8 


10 
SI 
12 


168 


171 


171 


177 
207 




196 


200 


232 
261 


22 1 
252 
280 

336 


257 
285 
314 

812 


854 


360 






378 









INTEREST TABLE. 



81 



Interest Table at 6 Per Cent.— Continued. 



Days, 


DOLLARS. 


67 


68 


69 


70 


71 


72 


73 


74 


75 


76 


77 


1 
2 


l 


i 


i 


i 


i 


i 


i 


i 


i 


i 


1 


2 


2 


2 


2 


2 


2 


2 


2 


2 


2 


3 


3 


3 


3 


3 


4 


4 


4 


4 


4 


4 


4 


4 

5 


4 


4 


5 


5 


5 


5 


5 


5 


5 


5 


5 


6 


6 


6 


6 


6 


6 


6 


6 


6 


6 


6 


6 


7 


7 


7 


7 


7 


7 


7 


7 


7 


7 


8 


7 
8 


8 


8 


8 


8 


8 


8 


8 


9 


9 


9 


9 


9 


9 


9 


9 


9 


9 


10 




10 


10 


10 


9 
10 
11 
12 
13 


10 


10 


10 


10 


11 
12 


11 
12 


11 
12 


11 


11 


11 


11 


11 


11 


11 


12 




12 


12 


13 


12 


12 


12 


13 


13 

11 


13 

11 


13 






14 


14 


13 


13 


14 


14 


14 










14 


15 


15 


15 


15 


15 


16 


16 






16 


14 


15 


16 


16 


16 


16 


17 


17 


17 


17 


19 


19 


15 
16 
17 


17 


17 


17 


17 


is 


19 


18 




18 


18 


18 


18 


19 
20 
21 

22 


10 






21 
22 


22 


19 


19 


19 


20 

21 


20 


21 


18 
19 
20 
21 


20 


20 


20 


21 
22 




21 


21 


22 


23 








24 


24 


22 


22 . 


23 


28 




21 
25 


24 


24 




25 




23 


24 


24 


25 


25 
26 

27 

28 








22 


25 


25 


25 


26 




27 


27 






28 


23 
24 
25 


26 


26 


27 


27 


28 


28 


28 


29 




30 


27 


27 


28 


28 










30 


31 


28 


28 


29 


29 


30 


30 


30 






32 


32 


26 
27 

28 
29 


29 


29 


30 


30 


31 








33 


33 


30 


31 


31 






32 






34 


34 


33 


31 


32 


32 


33 


33 






35 


35 


35 


36 


32 


33 


33 


34 


34 




35 36 


36 


37 


37 


30 

Mos. 


33 


34 


34 


35 


35 


36 


36 


37 


37 


38 


38 
















1 






33 


34 


34 


35 


35 


36 


36 


37 


37 


38 


38 


o 


67 


68 


69 


70 


71 


72 


73 


74 


75 


76 


77 


3 


101 
134 


102 


104 


105 


107 


108 


110 


111 


113 


114 


116 


4 


136 


138 


140 


142 


144 


146 


14S 


150 


152 


154 


5 


168 


170 


173 


175 


178 


IN) 


183 


185 


188 


190 


193 


6 


201 


204 


207 


210 


213 


216 

252 


219 
"256 


222 
259 


225 


228 


231 


7 
8 


235 


238 


242 


245 


249 


263 


266 


270 


268 


272 


276 


280 


284 


288" 


292 


296 
333 


300 
"338 


304 

342 


308 
347 


9 


302 


306 


311 


315 


320 


324 


329 


10 
11 


335 


340 


345 


350 


355 


360 


365 


370 


375 


380 


385 


369 


374 


380 


385 


391 


396 


402 


407 


413 


418 


424 


12 


402 


408 


414 


420 


426 


432 


438 


444 


450 


456 


462 



82 



INTEREST TABLE. 



Interest Table at 6 Per Cent. — Continued. 



Days. 

1 
2 
:i 
l 
r> 
6 
7 
8 
!> 
10 

11 

12 
13 

11 
ir> 
16 
17 

IS 

19 
20 
21 


DOLLARS. 


78 


79 


80 


81 


82 83 


84 85 


86 


87 


88 


i 


1 


i 


i 


i 


1 


i 


1 


i 


i 


i 


3 


3 


3 


3 


3 


3 


3 






4 


4 


4 


4 


4 




4 


4 






4 


5 


5 


5 


5 


5 


:. 




6 






7 


G 


6 


7 


7 


7 


7 


7 


7 


7 










8 






- 


8 




10 

11 

14 


10 

L3 

11 


g 


9 


9 


9 


9 


10 


10 




lo- 


in 

12 
13 

11 
15 

17 


LO 
12 
13 

11 
L6 
17 
L8 
L9 
21 
22 
23 


11 


11 


11 


11 

12 

11 
15 
L6 
L8 

20 
22 
23 
25 


11 

12 
14 

15 

17 
18 
L9 
21 
22 

26 
299 

29 
:;i 
32 
84 


11 
13 

11 

17 
L8 

21 


ll 
13 

U 


12 
L8 

11 
L6 
17 
L8 
20 
21 
22 
24 


12 
L3 
15 
16 

17 
L9 

21 


12 
L3 

i:> 
L6 

19 
20 
22 


16 

17 
18 
20 

2\ 


16 

17 
11) 

L>1 

24 

21 


16 

17 
19 

29 

11 
i:; 
44 


18 
19 
21 
22 
23 


2\ 


23 
24 

27 

:;i 
32 
34 


24 


24 


24 
26 

21 
29 

:;i 
32 
34 
35 


25 
26 

29 

32 

:;i 


25 
26 

:;i 


•j.; 
27 
29 

:;i 

84 

87 


26 

•-'7 
29 

87 


27 
28 


27 




11 

43 


22 

2:* 

21 
25 
26 
27 
28 
29 


81 




86 
38 

11 
12 


87 

10 
41 

12 


87 

10 

12 

i:; 


36 






39 


:;7 
39~ 


40 


10 


40 

11 


LO 

11 


:*o 


Mos. 

I 

2 

:j 
4 
5 

6 

7 






















39 


89 






41 
82 
V2:\ 
164 
205 
246 


11 

125 
166 

249 


12 
M 
126 

210 
252 


42 

85 

170 
213 


43 

129 
172 
215 

301 
344 

430 


-7 
131 

171 

261 


n 

132 
176 

264 

440 
184 


78 


71) 




M 
122 
162 

243 
284 


117 
156 


119 
158 


120 
160 
200 

2 10 


195 
234 


198 
237 


1273 


•J77 


280 


287 


291 


294 


340 


8 


312 
351 


316 


320 


324 






10 
11 
12 


356 


360 


365 


369 


374 




425 


390 


895 


400 


405 


410 


415 


420 


429 


435 


440 


lie. 


151 


457 


462 






171) 


468 


474 


ISO 


486 492 41)8 


504 510 


516 







INTEREST TABLE. 



83 



Interest Table at 6 Per Cent— Continued. 



Days. 


DOLLARS. 


89 

i 


90 


91 


92 


93 


94 95 


96 


97 


98 


99 


1 


i 


i 


2 


2 


2 2 


2 


2 


2 


2 


2 
3 
4 


3 


3 


3 


3 


3 


3 3 


3 


3 


3 


3 


4 


4 


4 


5 


5 


5 5 


5 


5 


5 


5 


6 


6 


6 


6 


6 


6 6 


6 


6 


6 


7 


5 

6 


7 


7 


7 


8 


8 


8 8 


8 


8 


8 


8 


9 


9 


9 


9 


9 




9 


10 


10 


10 


10 


7 


10 


10 


10 


11 


11 


11 


11 


11 


11 


11 


12 


8 


12 


12 


12 


12 


12 




13 


13 


13 


13 


1 


9 
10 
11 
12 
IS 


13 


13 


13 


14 


14 


11 


14 


14 


15 


15 


15 


15 


15 


15 


15 


15 




16 


16 


16 


16 


16 


16 


16 


16 


17 


17 


17 


17 




18 


18 


18 


18 


18 


18 


18 


19 


19 
20 


19 


19 


19 


20 


20 


19 


19 


19 


20 




21 


21 


21 


21 


21 


14 


20 


21 


21 


21 


22 


22 


22 


22 


_ 


23 


_ 


15 
16 


22 


22 


22 


23 


23 


23 


■2 \ 
- 

27 




_ 


24 


25 


23 


24 


24 


24 






26 


26 


17 

" 18 


25. 


25 


25 






27 


27 


27 


28 


28 


26 


27 


27 


27 








30 


19 
20 
21 




28 


28 


29 






30 






31 


31 
33 


29 


30 


30 


30 


31 




31 


31 


32 


32 




33 








34 


35 


22 


33 


33 


33 


34 


34 




35 






36 


36 


23 
24 
25 
26 
27 


34 


35 


35 




36 


36 




37 


38 




36 


36 


36 • 


37 


37 


38 


38 


39 


39 


40 


37 


38 


38 


38 


39 


39 40 


40 


40 


41 


41 


39 


39 


39 


40 


40 


41 


41 


4J 




42 


43 


40 


40 


41 


41 


42 


42 


43 


43 


44 


44 


45 


28 


42 


42 


42 


43 


43 


44 


44 


45 


45 


46 


46 


29 


43 


44 


44 


44 


45 


45 


46 


46 


47 


47 


48 


30 


44 


45 


45 


46 


46 


47 


47 


48 


48 


49 


49 


Mos. 
l 

2 
























44 


45 


45 


46 


46 


47 47 


48 


48 


49 


49 


89 


90 


91 


92 


93 


94 95 


96 


97 


98 


99 


3 


134 


135 


137 


138 


139 


141 142 


144 


145 


147 


148 


4 


178 


180 


182 


184 


186 


1S8 190 


192 


194 


196 


198 


5 


223 


225 


228 


230 


232 


235 


237 


240 


242 


245 


247 


6 


267 


270 


273 


276 


279 


282 


285 


288 


291 


294 


297 


7 


312 


315 


319 


322 


325 


329 


332 


336 


339 


343 


346 


8 


356 


360 


364 


368 


372 


376 380 


384 


388 


392 


396 


9 


401 


405 


410 


414 


418 


423 427 


432 


436 


411 


445 


10 


445 


450 


455 


460 


465 


470 475 


480 


485 


490 


495 


11 


490 


495 


501 


506 


511 


517 522 


528 


533 


539 


544 


12 


534 


540 


546 


552 


558 


564 ! 570 


576 


582 


588 


594 



84 



INTEREST TABLE. 



Interest Table at 6 Per Cent— Con tinned. 



Days. 

1 




DOLLARS. 


100 


200 300 400 500 600 700 800 900 


1000 2000 








7 


12 






2 


3 
















10 








7 












6 




17 










7 
8 
i) 
lo 
11 
12 
18 
It 
ir> 
16 
17 
IS 
19 
20 
21 

2:* 
2 1 
25 
2 (J 
27 
28 
29 


12 
13 
15 

17 

22 






70 

L10 
120 


110 




117 








. 


175 

1-7 






























147 






-117 




12 

i.; 


77 




217 
















17 




145 


187 














30 

Mos. 






























1 

2 








































3 








4000 


4 






5 






6 

7 
8 








350 


1 : 






400 


800 2000 2 




10 




900 






500 




11 
12 








600 


3000 3600 4200 4800 5400 







COMPOUND INTEREST. 85 

Compound Interest by Decimals, at 7 Per Cent., from One 
Year to Ten Years. 

Principal, 100 cents. 

1.07 — 1 year. 
1.1449 — 2 years. 
1.225043 — 3 years. 
1.31079601 — 4 years. 
1.4025517307 — 5 years. 
1.500730351849 — 6 years. 
1.60578147647843—7 years. 
1.7181861798319201 — 8 years. 
1.828459212420154507 — 9 years. 
2.01130513366216995770— 10 years. 

Table of Compound Interest at 6 Per Cent. 

Principal, 100 cents. 

1.06 — 1 year. 
1.1236 — 2 years. 
1.191016 — 3 years. 
1.26247699 — 4 years. 
1.3382255776 — 5 years. 
1.418519112256 — 6 years. 
1.50363025899136— *7 years. 
1.593S48074530S416 — 8 years. 
1.689478959002692096 — 9 years. 
1.79084769654285362176 — io years. 
1.8982985583354248390656— 11 years. 
2.01219649835550329409536 — 12 years. 

Use of the Above Tables. — Required the compound 
interest of $100, for 10 years, at 6 per cent. 
Ans. — $79.08.4 mills. 

1.7908476 tabular number. 

100 X by the principal. 
179.0847600 

100 subtract the principal. 

79.08.4 



86 



INTEREST. 





o 


1 ° 


1 ° 


1 -■ 


1 T—l 


1 -H 


rH 


| CM | CM 


CM 


| :7 


I ct 


CO 


X 


oa 






1 ° 


1 ° 


1 rH 


1 '""' 


1 «-' 


1 r " 1 ' 


| 71 j 71 


71 


CO 


1 :t 


CO 


1 * 


1 °* 




CO 


1 ° 


1 ° 


1 rH 


1 ^ 


1 ^ 


1 ^ 


1 T1 


1 T1 


-M 




| CO 


77 


1 ~ 


1 cr * 




COC- 


1 ° 


o 


1 ^ 


1 r " 1 


1 ,— ' 


1 - 1 


CM 


71 


71 


CM 


CO 




CO 


OS 




«^lo 
coco 


o 


o 


1 rH 


1 1 ~" ' 


1 r ~ ( 


1 ,_H 


CM 


71 


[ CM 


71 


1 ~1 


co 




I*' 




1 ° 


o 


i rH 


1 '"" ' 


1 ^ 


1 ^ 


71 


71 




71 


CM 


77 


»-7 


00 




OH 


o 


© 


1 1 " H 


1 ' — ' 


1 ^ 


1 ^ 


71 


71 


71 


1 ^ 


1 7} 


1 W 


1 l ~ 


1^ 




cn 

CO 


1 ° 


o 


1 ,_H 


1 r-( 


1 -■ 


- 


1 ~ ] 




71 


71 


71 


1 N 


1 iT; 


t— 




CO 
CO 


- 


o 


1 ° 


I— 1 


I— ( 


^ 


71 


: i 


71 


CM 


1 N 


71 


: 


I- 




co 


o 


o 


1 ° 


1 ° 


rH 


.—1 


-. ! 


71 


71 


71 


71 


71 




t^ 




CO 
CO 


~ 


o 


1 ° 


1 ° 


1 *4 


~ 


•H 


1 rH 


71 


71 


71 


71 








COCO 


o 


~ 


1 c 


; - 


- 


1— < 


- 


1 '- 


71 




: i 




-r 


CO 




CO 

CO 


c 


o 


1 ° 


© 












71 


71 


CM 


— 


c 




HC1 

coco 


c 


o 


1 ° 


1 ° 












71 


71 


CM 


-t< 


CO 


4-^ 


o 

CO 


o 


o 


1 ° 


c 












71 


71 


71 


— 


iC 


CD 


OOCD 

cooq 


o 


o 


1 ° 


o 












71 


CM 


CM 


t* 


lO 


*H 
CD 

PL, 


CM 

CD 
CM 


o 


o 


o 


~ 
















71 






c 


o 


- 


o 






















CD 


CO 


o 


o 


o 


r 
















:i 


CO 


•7 


"8 


COr^ 

coco 

.-ICO 

coco 


, 3 
o 


o 


c 


> 


r 


















CO 


-r 


<D 




o 


















CO 


<<* 


g 


C50 
rHCSJ 


o 


© 


o 


o 


o 
















CO 




CO 

H 


o 


o 


o 


o 


o 
















CM 




PI 


i— 1 


o 


o 


o 


3 


- 
















71 


CC 




CO 
f— 1 


o 


o 


o 


o 


o 


o 














CM 


jfj 




H 


o 


o 


o 


o 


o 


o 














CM 


CO 




^ 


o 


o 


o 


c 


o 


o 


o 


















00 

r-H 

co 


o 


o 


o 


o 


o 


o 


o 












CM 


w 




o 


~ 


- 


o 


o 


o 


o 


o 












71 




rH 
r-H 

O 
I— 1 


o 


o 


c 


o 


o 


o 


o 


o 


o 


rH 


i— i 


rH 


rH 


71 




© 


o 


o 


© 


o 


o 


o ' 


- 


o 


O 


—i 


rH 


rH 


71 




C5 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


— 


rH 


i—i 


71 




c^co 


o 


o 


o 


o 


. o 


o 


o 


o 


o 


o 


O 


O 


1— 


71 




LOCO 


o 


o 


o 


© 


o 


o 


o 


o 


o 


o 


© 


o 


•H 


i-n 




COrdH 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


•o 


O 


- 






T- 




s\ 




*1 




<* 




>: 




c 


L- 




X 




Ct 




e 

H 




H 




H 




?1 







INTEREST. 



87 






3 - 
£ '-> 

- -J 



C75 


1 ° 


rl 1 H 


01 


CI 


| CO 


1 °° 


1 ^ 


| -H 


| id 


1 * 1 « 


3 12 


ooo 


O 


1 -? 1 — ■ 


oi 


01 


co 


CO 


rH 


^ 


lO 


<o 


LO 


22 IS 


CO 


© 


I— 1 


1 ^ 


?! 


CI 


co 


i M 


rH 


th 


lO 


LO 


LO 


in 


o 


rH 


rH 


<N 


CI 


co 


CO 


<# 


-H 


lo 


lO 


LO 


3 is 


CD CD 


o 


1 -* 


r-i 


01 


N 


00 


CO 


rH 


^ 


LO 


LO 


LO 


a is 


CO 


o 


rH 


r-i 


01 


cq 


CO 


CO 


*$ 


^H 


LO 


lO 


LO 


3 |S 


OH 
COCO 


o 


iH 


rH 


N 


cq 


CO 


CO ' 


-r 


HH. 


LO 


iO 


LO 


s is 


00 CD 
0000 


o 


rH 


rH 


CM 


eq 


CO 


CO 




CO 


rH 


LO 


LO 


>o 


2 IS 


00 


o 


rH 


rH 


CM 


ci 


CO 


CO 


SO 


rH 


«t 


iO 


LO 


© 1 CD 

i— 1 r— 


CD 
00 


o 


rH 


r-l 


cm 


ci 


CO 


CO' 


CO 


^H 


^H 


LO 


LO 


O 1 LO 


0000 


o 


rH 


rH 


CM 


<N 


CO 


CO 


DC 


~H 


rH 


LO 


LO 


O 1 LO 


CM CO 

0000 


o 


rH 


rH 


01 


03 


CM 


CO 


CO 


— M 


— 


LO 


L0 


O 1 LO 


rH 
00 


o 


rH 


rH 


oq 


CI 


CM 


cc 


CO 


-H 


rH 


rH 


LO 


O 1 LO 


O 

00 


o 


rH 


rH 


<N 


CI 


01 


CO 


CO 


-rH 


rH 


rH 


LO 


O 1 H- 


OOC35 


o 


rH 


r-i 


N 


01 


01 


CO 


CO 


rH 


rH 


- 


LO 


© | 2 




o 


rH 


r-i 


(N 


<M 


01 


CO 


CO 


CO 


rH 


rH 


L0 


• 12 


toco 


o 


rH 


rH 


CM 


CI 


01 


CO 


CO 


CO 


rH 


rH 


LO 


• 12 


o- 


o 


rH 


rH 


rH 


Ol 


01 


CO 


CO 


CO 


rH 


rH 


rH 


~ 1 2 


CSJOO 


o 


rH 


rH 


r-i 


CI 


01 


CO 


CO 


CO 


rH 


rH 


-r 


o | 2 


rH 


o 


rH 


rH 


rH 


01 


CM 


Ol 


CO 


CO 


^ 


rH 


rH 


o | £ 


O 


o 


rH 


r-{ 


rH 


CM 


01 


CM 


CO 


CO 


rH 


rH 


rH 


00 | 2 


00 CD 

coco 


o 


rH 


rH 


rH 


CM 


CM 


Ol 


CO 


CO 


CO 


rH 


rH 


°° 1 2 


coo- 
coco 


o 


rH 


- 


rH 


CM 


CM 


Ol 


CO 


CO 


CO 


rH 


rH 


x is 


"^LO 

coco 


o 


rH 


rH 


rH 


CM 


CM 


CM 


CO 


CO 


CO 


CO 


rH 

rH 


» IS 
« 13 


CO 
CO 


o 


rH 


r-i 


rH 


CM 


Ol 


Ol 


CO 


CO 


CO 


CO 


rHcq 
coco 


© 


r— ( 


rH 


- 


CM 


Ol 


01 


c: 


CO 


CO 


CO 


rH 


^ 13 


CDO 
IOCO 

00 
LO 


o 


rH 


r-i 


rH 


CM 


CM 


CM 


CM 


CO 


CO 


CO 


rH 


*- 12 


© 


rH 


■"• i 


1—1 


CM 


Ol 


Ol 


Ol 


CO 


CO 


CO 




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LO 


o 


rH 


rH 


rH 


rH 


00 


CM 


CM 


CO 


CO 


CO 


CO 


t- 


2 


LOCO 
LOLO 


o 


rH 


r-i 


rH 


r-i 


CM 


CM 


oq 


CO 


CO 


CO 


CO 


£- 


2 


OOHH 
LOLO 


o 


rH 


r-i 


rH 


r-i 


CM 


C<1 


CM 


CM 


CO 


CO 


CO 


• IS 


rHCS] 1 
LOLO 1 ^ 


rH 


rH 


rH 


r-i 


Ol 


CM 


Ol 


oi 


CO 


CO 


CO 


O | © 




r" 




8 


' 


ft 




^ 




K 




S 




t- 




X 




Ci 






H 




H 








<* 




CO 



-• - 

3 I 
DO 9Q 



s i 





an 


— 
- 






~ 




-o 


~ 


- 


— 


O 


- 




- 










a 


:■ 


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•_ 


~ 


N 


r. 


r" 


a 


— 
- 



- 15 



S 



< r 

rl S 

S3 



88 INTEREST. 

Simple Interest. 
What is the interest on 8942.29, for one year, at 6 per 

Cent,? 100 : 6 :: 942.29 

6 



100 ) 5653.74 ( 56.5374 = $56.53^. 

Mules for Calculating I 

To find the interest on any principal for any number of 
days, the answer in each case being in cents, separate the 
two right hand figures of answer to express in dollars and 
cents. Rule as follows : 

For 4 per cent. — Multiply the principal by the number 
of days to run, separate the right hand figures from the 
product, and divide by 9. 

For 5 per cent. — Multiply by the number of days, and 
divide by 72. 

For 6 per cent. — Multiply by the number of day-, sepa- 
rate flight hand figure, and divide by 6. 

For 8 per cent. — Multiply by the number of days, and 
divide by 45. 

For 9 per cent. — Multiply by the number of days, s» pa- 
rate right hand figure, and divide by I. 

For 10 per cent — Multiply by the number of day-, and 
divide by 36. 

For 12 per cent. — Multiply, by the number of days, sepa- 
rate right hand figure, and divide by •>. 

For 15 per cent. — Multiply by the number of days, and 
divide by 24. 

For 18 per cent. — Multiply by the number of days, sepa- 
rate the right-hand figure, and divide by 2. 

For 20 per cent. — Multiply by the number of days, and 
divide by 18. 

For 24 per cent. — Multiply by the number of days, and 
divide by 15. 



INTEREST. 



89 



A Table Showing the Amount of $100, at Compound 
Interest, at 6 Per Cent. 



1 year 

2 years 

3 " 

4 " 

5 " 

6 " 



$106.00 
112.36 
119.10 
126.24 
133.82 
141.85 



7 years . 






8150.36 


8 " . 






159.38 


9 " . 






168.95 


10 






179.08 


11 " . 






189.82 


-12 " . 






201.21 


• • • 


402 


. 




804 


, , 




. 1608 


, , 




. 3216 


. 




. 6432 


, . 




. 12864 


. . 




. 25728 


. , 




51456 


. . 




102912 


. 




205824 


. 




411648 


hundred a 


'ears 


amount to 13 



Second term of 12 years 

Third " " " " 

Fourth " " " " 

Fifth " " " " 

Sixth " " " " 

Seventh " " " 

Eighth " " " 

Ninth " " " " 

Tenth " " " " 

Eleventh" " " " 

Twelfth " " " " 
and at this rate would in two hundred y< 
millions, and in three hundred years, to about 4 thousand 
millions of dollars. 

If I purchase of National bank-stock, that produces a 
half-yearly dividend of 4A per cent., 100 shares, par $50 each, 
$5000, at 30 per cent, advauce, for which I pay in cash $6500, 
required how much per cent, per annum I get on the money 
advanced. 

Interest on the stock for 12 months, 8450.00 

Interest on the interest for 6 months, 10.12^ 

So the $5000 stock, or $6500 cash, has produced $460.12* 
in one year. 

•Now say, as the money the stock cost, $6500, is to the in- 
terest of the stock for one year, $460.12^, so is $100 to its 
8* 



90 



DISCOUNT. 



interest for one year, which gives 87.070 per cent, per annum 
nearly. 

Proof.— Multiply $6,500 by 87.079, which equals S-k'0.13. 



Discount 

Is the deducting of a sum for the prompt or advanced 
payment of obligations, notes, etc. Most persona deduct the 
rate per cent, from the sum for the discount ; banks also. 

Although practice makes it common, this system is con- 
trary to equity. 

The sum deducted should be such that the balance at the 
rate per cent, given would amount to the original. 

The rule is as loo, with the rate per cent, added, is to the 
rate per cent, so is the sum given to the discbunt; that is, 
106: 600:: 100: 566^, or x by 3/4-53. 

In the other case, If $6 are deducted, the charge is more 
than per cent. 



Table of the Approximate Value of Foreign Coins in 
United States Currency. 



Augustus, Saxony. 

Oarolin, Bavaria 4.93 

Copeck, Russia 

Crown, Baden, Bavaria*— 1.06 

Crown, or 5s., English 1.13 

Crown, Portugal 1.12 

Crown, Sardinia 92 

Crown, Sicily 96 

Crown, Spanish, half pis- 
tole 1.95 

Dollar, Central America.. .95 
Dollar, Chili, Mexico, 
Peru, Bolivia, New Gra- 
nada 1.00 



Dollar, Norway, Sweden, 

Spain $1.05 

Dollar, Ri gsbai ik, I ten ma rk, 
Dollar, Specie-] tollar, Den- 
mark 1.05 

Doubloon, Centra] Amer- 
ica $14.50 to I 

Doubloon, New < rranada.... I 
Doubloon, Spain, Mexico.... 15.65 

Drachm, Greece 18 

Dncat, Austria, Bohemia, 

Hamburg, Hanover 2.28 

Dncat, Denmark LSI 

Ducat, Sweden 2.20 



VALUE OF FOREIGN COINS, 



91 



Ducatoon, Holland $1.32 

Florin, Austria, Silesia... .48 
Florin, (gold) Hanover... 1.66 
Florin, (silver) Hanover .56 
Florin, Holland, Nether- 
lands, South Germany.. .40- 

Florin, Prussian 55 

Franc, France and Bel- 
gium 19 

5-franc piece 95 

Guilder, British Guiana.. .26 

Guilder, Netherlands 40 

Guinea, 21s., English 5.08 

Gulden, Baden 40 

Groschen, Poland, Prussia .02^ 

5Groschen 12 

Grote, Bremen 01 

Imperial, Russia 7.92 

10 Kreutzer, Austria 08 

60 Kreutzer, or Florin, 

Austria 48 

Kreutzer, Bavaria , % 

Lira, Milan 14 

Livre, France, Sardinia... .183^ 
Livre, Tuscany, Venice... .16 

Marc, Denmark 09 

Maximilian, Bavaria 3.30 

Milrea, Portugal 1.12 

Mohur, Bengal 8.15 

Mohur, Bombay 7.28 

Moidore, Portugal 6.50 

Napoleon, 20 Francs, 

France 3.S4 

Ounce, Sicily 2.50 

Paolo, Rome 10 

Para - 9 - 

Peseta, Spain 20 

Pound, Canada, New 
Brunswick, etc 4.00 



Pound, English $4.84 

Pistareen, Spain 20 

Piastre, Egypt 05 

Piastre, Spain 1.04 

Piastre, Turkey, old 42 

Piastre, Turkey, new 04 r 2 g- 

Pistola, Rome 3.37 

Pistole, Spain 3.90 

Reale, Central America, 

average 05% 

Reale Plate, Spain 10 

Reale Vellon, Spain 05 

2 Reales, Ecuador 18% 

Reis (1200), Brazil 99 

Rix-Dollar, Bad en, Bruns- 
wick 1.00 

Rix-Dollar, Bavaria, Aus- 
tria, Hungary 97 

Rix-Dollar, Hanover 1.10 

Rix-Dollar, Sweden and 

Holland 1.05 

Rouble, Russia 79 

5 Roubles, Rus.-ia 3.95 

Rupee 53 

Rupee, Bombay, Ma- 
dras 45 

Schilling, Hamburg 02 

Scudo, Genoa 1.28 

Scudo, Naples, Sicily 95 

Scudo, Piedmont 1.36 

Scudo, Rome 1.00 

Scudo, Sardinia 92 

Shilling, English 23 

Skilling, Denmark % 

Sou, France, nearly 01 

Sovereign, English 4.84 

Sovrano, Austria, Bohe- 
mia 3.57 

Specie thaler, Saxony 98 



92 REDUCTION OF FOREIGN MONEY 



Star, Pagoda, Madras $1.81 

Stiver, Holland, nearly 02 

. Teston, Rome 30 

Testoon, Portugal 12 

Thaler, N. Germany, Bre- 



men, Saxony, Hanover, 

Poland S .69 

10 thaler, Prussia 8.00 

Zcvhin, Turkey 1.40 

Zecchino, Rome 2.27 



The United States coins are: Copper — ?■_•, 1, and '2 cents. Nickel 
and copper — 1,3, and 5 cents. Nickel and silver — 3 cents. Silver 
— half-dime = 5 cents ; one dime = 10 cents ; two dimes — 20 cents; 
quarter-dollar =25 cents; half-dollar ts; Legal-tender dollar, 

412} grains; trade-dollar, 430 grains. Gold — 1 and 3 dollars; quar- 
ter-eagle = 2.50 ; half-eagle 5.00; eagle L0.00, and doable < 
= 20.00. 

The deDominatioa of U. 8. money, called Federal money, 
from the confederation of the States, was established by act 

of Congress in the year 176"), and are eagle, dollar, dime, 
cent, and mill. 

Rule to reduce or change Canada currency to Federal 
money. — Reduce to pence and divide by 60. 

Rule to reduce British Sterling to dollars and cents. — In- 
duce it to 6 pence and divide by 9, because nine sixpeii 

make one dollar, and |4.4 1.1 l\ 8. money =£1 sterling. 

Example. — £ *. d. 

1 
20 

20 

2 



9)40 



$4.44.4 



4 farthings = 1 penny, 12 pence — 1 shilling, and 20 shillings 
= one £. 

To reduce Sterling to dollars and cents, valuing the pound, 
with exchange added, at $4.80 to the given pound. — An- 
nex the shillings and pence in decimals of a pound, and 



INSURANCE. 93 

add a cipher, or move the decimal point one place to the 
right; then multiply by 8 and the product by 6, and the 
last product is the value in dollars and cents. 

To reduce or change Federal money to Sterling or English 
money. 

Example. — Multiply the cents by 54, cut off two figures 
to the right, and you have pence. 
Example.— $4.44.4 

54 
1776 
2220 
24 



12)240pp 



2p)2p 



£1 

To reduce dollars and cents to pounds at the rate of 
$4.80 to the pound. — Divide the given sum by 8 and the last 
quotient by 6 ; placing the decimal point one place to the 
left gives the required sum in pounds and decimal parts. 

To reduce any sum of French francs and centimes to 
dollars and cents. — Take |, and A of this %, and add the two 
together for the value required in dollars and cents. 

To reduce any sum in dollars and cents to francs and cen- 
times. — Multiply the given sum by 4, and to this product 
add one-third of it for the value required. 



Insurance. 
Insurance is a premium or percentage paid to a company 
for insuring against losses by fire or transportation. The 
company or underwriters issue to the insurer a policy of in- 



94 AVERAGES. 

surance, which contains the conditions of the contract ; the 
losses are regulated by the amount of damage, and paid ac- 
cordingly. 

If the damage is on land, settlements are made without 
much delay. 

If the loss is on the sea, there La sometimes considerable 
delay in the settlements, which are called av 

Trading vessels arc generally held on shares. The man- 
ager, or ship's-husband, being part owner, is allowed a percent- 
age on the amount of freight. The settlements are made the 
same as other partnership concerns; but in the settlement of 
losses, an important operation frequently occurs in settli 
averages, which are clai ral and particular, also 

called gross and simple. 



Averages. 

General average is a proportion paid by the propri 
for losses that are made with a view to safety — cutting away 
masts, etc., and throwing cargo overboard. 

Particular average La a contribution for Buch damagi 
may happen from common accidents at ><>a. This is paid by 
the proprietors of the articles which Buffered the dam: 1 
and the calculations are made according to the rules of Fel- 
lowship. 

In computing general average for cutting masts, el 
deduction of one-third is made from the cost, as new arti- 
cles are presumed to he that much better; hut goods thrown 
overboard are valued at the sum they would have netted 
had they arrived safely. 

When a ship's cargo and freight are fully insured, the 
underwriters are responsible to the proprietors for both gen- 
eral and particular averages. 






GENERAL AVERAGE. 95 

Example. — Suppose the ship Grey Eagle, from the West 
Indies to Philadelphia, in the course of her voyage, to have 
suffered the following damages : required the general and 
particular averages. 

General Average. 
Cost of replacing masts, cables, etc., cut away, 81500 

Deduct one-third for newness, . . . 500 1000 

Anchor lost, which cost 200 

10 puncheons of rum thrown overboard . . . 1000 

Sundry charges for pilotage, etc., .... 200 

Amount of general loss . . 82400 

Particular Average, 
Of 80 hhds. of sugar shipped, a part was so much dam- 
aged that the deficiency in 20, on a comparison with 60 that 
arrived safely, was 10 hhds., which at 8120 each amounted 
to $1200. 

SniP, CARGO, AND FEEIGHT. 

Grey Eagle valued at 822000 

Cargo, net proceeds ...... 34000 

Gross freight « 10000 

Portage bill deducted .... 200 9800 

Total amount .... 865800 

Statement of General Average. 
As 65,800 : 2,400 : : 100 : 3.65. 

Statement for Particular Average. 
As the value of 80 hhds. of sugar, which is 9,600 : 1,200 : : 
100 : 12.50. 

So the underwriters or insurers will have to pay 3.65 per 
cent., nearly, for general average on $65800, and 12.50 per 
cent, for particular average on 86600. 



96 FELLOWSHIP. 

Fellowship. 

Is a method of showing the gains or losses of parties in 
joint operations. 

Rule. — As the whole stock is to the whole gain or h 
is each share to the gain or I< 

Example. — Three persons purchase a factory for $100,000, 
A agreeing to subscribe $10,000; B,$40,000; C, $50,000, after 
the purchase. An offer ifl made by D, of $150,000, and ac- 
cepted by them. Required the shaft h in the profit. 
100000: 50000:: 10000: 5,000, A's aha 
100000: 50000:: 40000: 20,000, B*s u 
100000: 50000:: 50000: 25,00 \ ( 'a u 

Suppose they Bubscribe the amount, and manufacture 
goods for one year, and their profits net $50,000 at the end 
of the year. Required each one's capital. 

100000: 150000:: 10000: 15,000 A'a capital. 
100000: L50000:: 40000: 60,000 \Y> " 
100000: 150000:: 50000: 75,000 ("s " 

Double Fellowship, with Time. — Rule. — Multiply 
each share by the time of its interest in the fellowship; then 
as the sum of the products ifl to the product of each interest 

so is the whole gain or 1 ich share of the gain or 1 

EXAMPLE. — A ship's company take a prize worth 
810,000, which they divide according to their rate of | 
and time of service on hoard. 

The officers have been on hoard 6 months and the men 3 
months. The pay of the lieutenant- is $100, midshipmen 
$50, and men $10 per month ; and there are 2 lieutenants, 
4 midshipmen, and 50 men. What is each one's share} 
2 lieutenants, 8100 = 200 x 6 = 12»"> 
4 midshipmen, $50 = 200 x(i--= 1200 
50 men, 810 = 500 x 3 = MOO 

3900 



TABLES. 



97 



Lieutenants, 3900: 1200:: 10000: 3,076.92-*- 2 = 81,538.46 



Midshipmen, 3900 : 1200 : : 10000 : 3,076.92 



Men, 



3900 : 1500 : : 10000 : 3,846.16 -r- 50 = 



769.23 
76.92 



Weights and Measures. 

Diamond "Weight. 

16 parts = 1 grain = 0.8 Troy grains. 

4 grains = 1 carat = 3.2 " " 

The grain of diamond weight is equal to t 8 -q grain of Troy 
Weight. 

The carat equals 3^- grains of Troy Weight. 



Articles Sold by Number. 

12 units = 

12 dozen, or 144 units, = 

12 gross, or 1728 units, = 

20 units = 

Paper Measures. 

24 sheets = 

20 quires, or 480 sheets, = 

2 reams, or 960 sheets, = 



1 dozen, 
1 gross, 
1 great gross, 
1 score. 



1 quire, 
1 ream, 
1 bundle. 



Cloth Measures. 



2i inches 
4 nails 
4 quarters 



1728 cubic inches 
27 " feet 
9 



Cubic Measures. 



G 



1 nail, 
1 quarter, 
1 yard. 



1 cubic foot, 
1 " yard. 



98 WEIGHTS AND MEASURES. 

Book Measures. 

2 leaves are 1 folio, 
4 " " 1 quarto, 
8 " " 1 octavo, 
12 " " 1 duodecimo. 
To all sizes above these add mo, as, 16mo, 18mo, 24mo,etc. 

The standard measure of length for the United States and 
England is, theoretically, that of a pendulum vibrating E 
onds in the latitude of London, at a temperature of 6 
Fall., in a vacuum, and at the level of the sea. The length 
of the pendulum was originally supposed to be divided into 
39.1393 equal parts or inches, of which 36 inches were 
adopted as the standard yard. The original standard v. 
lost by fire in London, and could not he restored by pen- 
dulum, and at present the British yard measure is Bhoi 
than that of the United States by { \ of an inch in 100 feet 

Apothecaries' Weights. 

20 grains = 1 scruple, drains. Scruples. Drams. 
3 scruples = 1 dram = 60 
8 drams = 1 ounce — 480 = 2 \ 

12 ounces = I pound 5760 288 = 96 

In Troy and Apothecaries' Weights, the grain, ounce, and 

pound are the same. 

Troy Weights. 

24 grains = 1 dwt, Grains. Dwt 

20 dwt. = 1 ounce = 480 

12 ouuees = 1 pound = 5760 = 240 

Troy Weight is used for gold and silver. A cubic foot of 
pure gold is worth 8362600, and a cubic inch 8209.84. 

A cubic foot of pure silver is worth $12338, and a cubic 
inch $7.14; gold being worth about 29.39 times that of silver. 



WEIGHTS AND MEASURES. 



99 






= 1 lb., Avoirdupois, 

= 14-4 lbs. " 

= 192 ounces, Avoirdupois, 

= 1 ounce " 

= .8228+ lb. 

Avoirdupois "Weights. 

1 dram, 

1 ounce, Dram?. Ounces. Pounds. 

1 pound = 256 

1 cwt. = 28672 = 1792 

1 ton = 573440 = 35840 = 2240 

1 quarter, 

1 cwt., 
14 lbs. 

The standard Avoirdupois pound is the weight of 27.7015 
cubic inches of distilled water weighed in air, at the temper- 
ature of 39°. t 8 4 q, latitude of London; barometer, 30 inches. 



7000 Troy grains 


175 


" pounds 


175 


" ounces 


437, 


i " grains 


, 1 


" pound 


27- 


|| grains = 


16 drams 


16 


ounces = 


112 


pounds = 


20 


cwt. = 


28 


pounds = 


4 


quarters == 


1 


stone — 



Cubic or Solid Measures. 



1728 cubic inches 


1 cubic or solid foot, 


27 cubic feet 


• = 


1 cubic " yard, 


128 cubic feet, 


4x4x8 = 


1 cord of wood, 


24.75 " " 


= 


1 perch of stone, 


306 " " 


= 


1 rod, 


57.25 " " 


= 


1 chaldron = 36 bushels, 


42 " " 




1 ton of anthracite coal, 


46 " " 




1 " " bituminous " 




Scripture Long Measures. 




Feet. Inches. 


Feet. Inches. 


A digit = 


0.912 


A cubit = 1 9.888 


A palm = 


' 3.648 


A fathom = 7 3.552 


A span = 


10.944 





100 WEIGHTS AND MEASURES. 

Liquid Measures. 

Cubic Ins. 

4 gills = 1 pint = 28.875 

2 pints = 1 quart = 57.750 = 8 gills, 

4 quarts = 1 gallon=231. =32 " 

3H gallons = 1 barrel, 

42 gallons = 1 tierce, 

2 bbls., or G3 gallons, = 1 hogshead, 
2 tierces, or 84 gallons, = 1 puncheon, 
2 hogsheads = 1 pipe, or butt, 

2 pipes, or 252 gallons, =1 ton. 
• A standard gallon measures 231 cubic inches, and con- 
tains 8.3388822 lbs. Avoirdupois, or 58372.1754 Troy -rains 
of distilled water at 39° Fah., barometer at 30 inches. 

Dry Measures. 

2 pints = 1 quart, 

4 quarts = 1 gallon 

2 gallons = 1 peck 

4 pecks = 1 bushel 

36 bushels = 1 chaldron. 

The standard bushel is the Winchester, which contains 
2150.42 cubic inches, or 77.627413 lbs. Avoirdupois of dis- 
tilled water at its maximum density. 

Its dimensions are 1S\ inches diameter inside, V. )] , inches 
outside, and 8 inches deep; and when heaped, the cone 
must not be less than 6 inches high, equal to 2747.715 cubic 
inches for a true cone. 

A Gallon = 268.8025 cubic inches. 

A Struck Bushel = 1/24445 cubic feet, 

A Cubic Foot = .80356 of a Struck Bushel. 

A Barrel of Flour = 196 lbs. 

Many articles, as seed, grain, etc., although measured by 
the bushel, are really sold by weight. The following are 



Pinto. 


Quarts. Gallons. 


= 8 




: 16 


= 8 


64 


= 32 = 8 



HEAT. 



101 



thus measured : Blue-grass seed, 14 lbs. to the bushel ; Dried 
Apples, 33; Bran, 20; Oats, 35; Timothy, 45; Castor-beans, 
46; Hemp-seed, 44; Barley, 48; Buckwheat, 52; Corn on the 
cob, 70; Salt, 85; Rye, Flaxseed, Corn, and Onions, 56; Po- 
tatoes, Beans, Wheat, and Clover-seed, 60, etc. 

The Barrel is not a legal measure, excepting Flour, 196 
lbs., and Beef, Pork, and Fish, 200 lbs. The capacity of a 
barrel varies, and is supposed to contain, Cement, 300 lbs.; 
Rice, 600; Powder, 25; Potatoes, 2-j- bushels, etc. 



The Melting-Point of Metals and Effect on Bodies by Heat- 
Fahrenheit Thermometer. 



Cast-iron 27-34 

Tin 475 

Lead 594 

Zinc 740 

Brass 1900 

Fine Silver 1850 

Copper. 2160 

Fine Gold 19S3 

Bismuth 487 

Tin and Bismuth, equal parts 283 
Tin 3, Bis. 5, and Lead 2.... 212 

Platina 4593 

Antimony 955 

Gold, annealed. 2266 

Bed heat visible in davliaht 1077 



Heat of common parlor-fire. 790 
Boiling-point of mercury.... 630 
Boiling-point of linseed-oil. GOO 

Boiling-point of alcohol 174 

Boiling-point of ether 98 

Heat of human blood 98 

Vinous fermentation... .60 to 77 
Acetirication begins at 78° 

and ends at 88 

Phosphorus burns at 43 

Snow and Salt, equal parts... 

Strong wines freeze at — 20 

Brandy freezes at — 7 

Greatest cold produced — 90 

Mercurv melts — 39 



Fluids boil in vacuo with 124° less heat than under the 
pressure of the atmosphere. All solids absorb heat when be- 
coming fluid. The heat absorbed in liquefaction is given out 
again in freezing. 

Water may be cooled at 20°. 

Freezing water gives out 140° of heat, and when con- 
gealed to ice, the thickness of 
9* 



102 



HEAT, 



2 inches will bear infantry, 
4 " " " cavalry or light guns, 
6 " " " heavy field-guns, 
8 " " u 24-pounders on sledges, weight not 
over 1000 lbs. to a square foot. 



Table of the Temperature Required to Ignite Different 
Combustible Substances. 



Fulminating powder 374 

Phosphorus 140 

Bisulphate of carbon vapor. 300 

Fulminate of mercury 

Sulphur 400 

Equal parts of sulphur and 

chlorate of potash 395 

Gun-cotton 428 

Nitro-glyoerine 49 I 

Rifle-powder 

Gunpowder, coarse 

Picrate of mercury, Lead, or 

iron 

Aluminum L832 



Picrate powder, fortorp 
" musk 

( Sharcoal, the most inflam- 
mable willow used for 
powder 

Charcoal, made by distilling 
wood at 

Charcoal made at 600° 

Picrate powder, for cannon.. 7 1 r» 

Wry dry pine wood 

" " oak " 900 

Charcoal madi ( .'<m) 

" M 1800° 1100 

" u 2100° 1400 



Weight of Nails. 



Name. 


Length. 


No. PES Pound. 




Ins. 




3-pennv. 


1 




4 " 


V/a 




5 « 






6 " 


2 


17o 


7 " 


2H 


141 


8 « 


2X 


101 


10 M 


Vi 


68 


12 u 


3 


54 


20 " 


3H 


34 



WEIGHT OP METALLIC BALLS. 



103 



Weight of Metallic Balls. 



S ™ 

^2 




VI £ 


Si 


o 
OS 

< 


Us 


52 ^ 






o 
« 

H 
DO 

o 




Lbs. 


Lbs. 


Lbs. 


Lbs. 




Lbs. 


Lbs. 


Lbs. 


Lbs. 


H 


.026 


.021 


.019 


.017 


&4 


30.1 


24.1 


21.5 


19.8 


% 


.088 


.070 


.063 


.058 


b l A 


34.7 


27.7 


24.7 


22.7 


1 


.209 


.167 


.148 


.136 


5% 


39.6 


31.7 


28.3 


25.9 


IK 


.408 


.325 


.290 


.266 


6 


45.0 


36.0 


32.0 


29.4 


IK 


.705 


.562 


.501 


.460 


GK 


57.2 


45.8 


40.8 


37.4 


1% 


1.12 


.893 


.795 


.731 


7 


71.5 


57.2 


50.9 


46.8 


2 


1.67 


1.33 


1.19 


1.07 


7K 


88.0 


70.3 


62.6 


57.5 


2K 


2.38 


1.90 


1.69 


1.55 


8 


106. 


85.3 


76.0 


69.8 


2^ 


3.25 


2.60 


2.32 


2.13 


8K 


127. 


102. 


91.2 


83.7 


2% 


4.34 


3.47 


3.09 


2.83 


9 


151. 


121. 


108. 


99.4 


3 


5.63 


4.50 


4.01 


3.68 


9K 


178. 


143. 


127. 


117. 


3J4 


7.15 


5.72 


5.10 


4.68 


10 


208. 


167. 


148. 


136. 


3K 


8.94 


7.14 


6.36 


5.85 


10K 


241. 


193. 


172. 


158. 


3% 


11.0 


8.79 


7.83 


7.19 


11 


277. 


222. 


198. 


182. 


4 


13.4 


10.7 


9.50 


8.73 


UK 


317. 


253. 


226. 


207. 


4K 


16.0 


12.8 


11.4 


10.5 


12 


360. 


288. 


257. 


236. 


4K 


18.9 


15.2 


13.5 


12.4 












4% 


22.7 


17.9 


15.9 


14,6 


TL 


e weig 


it of balls is 


as the 


5 


2(>!o 


20.8 


18.6 


17.0 


cube 


3 of the 


ir diameters. 





Copper. 
To Ascertain the Weight of Copper. 
Rule. — Find by calculation the number of cubic inches 
in the piece ; multiply them by .32118, and the product will 
be the weight in pounds. 

Lead. 

To Ascertain the Weight of Lead. 
Rule. — Find by calculation the number of cubic inches 
in the piece; multiply the sum by .41015, and the product 
will be the weight in pounds. 



104 



STRENGTH OF ROPE. 
Brass. 



To Ascertain the Weight of Ordinary Brass Castings. 

Rule. — Find the number of cubic inches in the piece; 
multiply by .3112, and the product will be the weight in 
pounds. 

Table Showing what Weight a Hemp Rope will Bear with 

Safety. 



Circum- 
ference. 


Pounds. 


tun- 


Pounds. 


Circum- 
■ ace. 


Pounds. 


[ns. 




ing. 








1 


200 








7200 


VA 


312.5 




•J Ml',", 






\M 


450 


4 






8450 


Y\ 


612.5 




361 . 




911! 


2 


800 


I', 


4050 


7 




2! ,' 


1012.5 


-r, 


4512.5 




10512.5 


2M 


1250 


5 






11250 


^i 


1512.5 








12012.5 


3 


1800 


f>H 


6050 


8 




:\\ 


2112.5 




6612.5 







Rule. — Multiply the square of the circumference in 
inches by 200, and it gives the weight the rope will bear 
in pounds with safety. For the Btrength of a good hemp 
cable, multiply the square of the circumference by 12 

The specific gravity of a body is its weighl as compared 

with that of water at a temperature of G0 D Fah., and 30 
inches at sea level. 

At 60° pure water weighs 62.331 pounds avoirdupois 
cubic foot. 

To find the gravity of a body heavier than water, weigh 
it first in the air, then in water, and find the difference; the 
difference is what the body loses in water, and is the weight 
of a bulk of water equal to the bulk of the body. Then say 
as this difference: weight in air : : 1 : specific gravity of body. 



SPECIFIC GRAVITY 



105 



Table of Specific Gravities. 









Average Spe- 


: of a 


Metals. cine Gravity. 


cub. It. in lbs. 


Aluminum ...... 2.6 




Antimony 




. 6.70 


418 


oic .... 




. 




Bismuth .... 




. 9.74 


607 


Brass .... 




. 


•504 


Bronze — copper 8 parts, tin 1 3 


gun 




529 


Copper, cast . 




. 8.7 




Gold, cast pure, 2-1 carat 




. 19.258 


12 


Iron, cast 




. 7.15 


440 


Iron, wrought 




7.77 




Lead .... 




. 11.41 


711 


Mercury 




. li 2 


849 


Platinum 




. 21.5 


1342 


Silver .... 




. 10.5 


655 


Spelter, or Zinc 




. 7. 1 




Sted 




. 




Tin, cast 




. " 


459 


Woods Dry). 




Apple 79 


49 


Ash 








.75 


47 


Boxwood 








.96 


60 


Cherry . 








. 




Chestnut 








.66 


41 


Cork . 








.25 


15.6 


Ebony . 








1.33 


83 


Elm 








.56 


35 


Hemlock 








.40 


25 


Hickory 








.86 


53 


Lignum- Vitae 








1.33 




Logwood 








.91 


57 



106 



SPECIFIC GRAVITY. 



Avoracro Spo- Weight of a 
cilic Gravity, cub. It. in ll>s. 



Mahogany 








.85 


53 


Maple . 








.79 


49 


Mulberry 








.89 


56 


Oak 








.9-3 




Pine, White . 








.40 


25 


Pine, Yellow . 








.72 


45 


Poplar . 








.38 


24 


Spruce . 








.-4U 




Sycamore 








.59 


37 


Walnut . 








.61 


38 


Stones and Earths. 




Alabaster 2.7 


168 


Coal, Anthracite 








. 1.5 


93.5 


Coal, Bituminous 








. 1.35 


84 


Basalt . 








•J. it 


181 


Borax 








. 1.71 


107 


Brick, hard . 










150 


Chalk . 








. 2.5 


156 


Clay, rollers', dry 








. 1.9 


119 


Coke . 












Crystal, pure Quart 


z 






. 2.66 


165 


Diamond 








1.53 




Earth, dry 










80-92 


Earth, soft 










110 


Emerald 








2.7 




Felspar . 








2.5 


156 


Flint . 








2.6 


162 


Garnet . 








4.2 




Glass 








2.98 


186 


Gneiss . 








2.G9 


168 


Granite . 








2.69 


168 


Greenstone, trap . 








3 


187 



SPECIFIC GRAVITY. 



107 



Gypsum, Plaster of Paris 

Hornblende . 

Limestone and Marbles 

Mica 

Peat, dry, compressed 

Ruby and Sapphire 

Salt 

Salt, fine 

Sand 

Sandstone 

Shales . 

Slate 

Sulphur . 

Trap 

Topaz 

Gravel about the same as Sand. 



Average Spe- Weight of a 

cine Gravity, cub. ft. in lbs. 

2.31 144 

3.25 203 

2.75 172 

2.93 183 

20-30 

• 4.04 

55 

49 

2.G5 106 

2.41 150 

2.6 162 

2.8 175 

2 125 

3 187 
3.55 



Liquids. 



Alcohol, common 
Alcohol, pure . 
Ether 

Oil— Whale, Olive 
Petroleum 
Proof Spirit 
Turpentine 
Vinegar . 
"Water, pure Eain or 
Fahr., 30 in. Bar. 
Water, Sea, average 
Wine 
Wines, average . 



Distilled, at 32° 



.834 
.793 
.716 
.92 

.878 
.916 

.87 
1.080 

1.000 

1.028 

.992 

.998 



52.1 

49.43 

44.6 

57.3 

54.8 

57.2 

54.3 

68 

62.375 
64.08 
62 
62.3 



108 



SPECIFIC GRAVITY. 



Miscellaneous. 
Air, Atmospheric, at 60° Falir., and 
under the pressure of one atmos- 
phere, or 14.7 lbs. per square inch, 
weighs 5^t P art as muca as water 



Cific (iiavity. cub. It. in !l»s. 



at G0° 




.00123 


.0765 


Asphaltum .... 




1.4 




Carbonic Acid Gas is 11 times 


as 






heavy as air . 




.00187 




Cement 






70 


Charcoal, Pine and Oak . 






15-20 


Fat 


. 


.93 




Gutta-percha .... 


. 




61.1 


Hydrogen Gaa is 14.1 times lighter 






than air, lb times lighter than o 


xy- 






.-' :1 








Ice 




.'.il 




Ivory ..... 






114 


Lard 


. 


.95 




Lime. ..... 






11)0 


Naphtha 


. 






Nitrate of Potash, or Saltpetre . 


. 


200 




Nitrogen Gas, ..^ part lighter than 


a i r 






Oxygen Gas, /„ part heavier than 


air 


U36 


.0846 


Pitch 




1.15 


71.7 


Powder ..... 




1 




Rosin ..... 




1.1 




Snow, compacted by rain . 








Snow, fresh .... 


. 




5-12 


Tar ...... 


. 


1 


02.4 


Wax, Bees, average . 


. 


.97 


60.5 



Application of the Above. — When the weight of a 
body is required, find the contents of the body in cubic feet 
and multiply it by the factor in the table. 



WATER. 



109 



Gravitation. 

TABLE EXHIBITING THE RELATION OF TIME, SPACE, AND VELOCITIES. 



Seconds 
from be- 
ginning 
of descent 


Velocity ac- 
quired at end 
of that time. 


Squares. 


Space fallen 
in that time. 


Spaces. 


Spaces fallen 
through in last 
second of fall. 




Ft. 




Ft. 




Ft. 


1 


32.166 


1 


16.08 


1 


16.08 


2 


64.333 


4 


64.33 


3 


48.25 


3 


96.5 


9 


144.75 


5 


80.41 


4 


128.665 


16 


257.33 


7 


112.58 


5 


160.832 


25 


402.08 


9 


144.75 


6 


193. 


36 


579. 


11 


176.91 


7 


225.166 


49 


788.08 


13 


209.08 


8 


257.333 


64 


1029.33 


15 


241.25 


9 


289.5 


81 


1302.75 


17 


273.42 


10 


321.666 


100 


1608.33 


19 


305.58 


11 


353.832 


121 


1946.08 


21 


337.75 


12 


336. 


144 


2316. 


23 


369.92 



To find the velocity of a falling body, multiply the time 
in seconds by 32.166 for the velocity in feet per second. 



Water. 

Fresh water is 1 part oxygen and 2 parts hydrogen ; by 
weight, 88.9 oxygen, 11.1 hydrogen. One cubic inch at 
62°, barometer 30 inches, weighs 252.458 grains ; from this 
it expands either from cold or heat. The temperature of 32° 
reduces it to solid ice, which expansion is about T \> part of 
its original bulk as water, and this expansive force is suffi- 
cient to split iron water-pipes ; by this expansive force 
rocks are split, and walls that are not of sufficient depth in 
the earth, are lifted upwards and overthrown. 

Wood remains sound for centuries, under either fresh or 

salt water, if not exposed to the action of the air or strong 

currents. Hard water contains considerable lime ; water in 

lead pipes produces carbonate of lead, an active poison ; but 

10 



110 WATER. 

where lime is present in the water, it forms a coating inside, 
that prevents the poisonous formation. Many substances are 
held in solution, being extracted from the earth through 
which the water penetrates. 

Water is the sole product of the combustion of hydrogen 
in oxygen, or the atmosphere; according to Humboldt, 8 
parts by weight of O. and 1 part of H. It is the impor- 
tant compound of all chemical mixtures. It comprises the 
greatest part of the earth's surface in the form of oceans, 
seas, lakes, and rivers; and in the north and south poles, 
snow, ice, iceberg, and glacier rising in form of vapor to the 
atmosphere. It produces by condensation mist, rain, and 
snow, to be returned to their original condition, to go 
through the same process constantly until the end of time. 

In the vegetable kingdom it is ever present, varyii; 
proportion from 10 to 00 per cent.; dry wood contai 
per cent. The human body, weighing 150 pounds, contains 
110 to 120 lbs. of water ; the rocks contain it in more or less 
quantities, according to their construction ; gypsum, 20 per 
cent. 

Bain-water collected in cities or near manufacturing dis- 
tricts is never pure, because it partakes of and contains 
gases which are given oil' from, or developed by, the com- 
bustion of coal, etc., forming compounds of sulphur and 
other substances. 

After thunder-storms the rain-water is always found to 
contain minute quantities of nitric acid, produced from the 
component parts of the air, nitrogen and oxygen, combining 
from the action of the lightning. 

Rain-water almost always contains a little organic matter, 
and it will become putrid after standing some time; organic 
substances are taken up into the clouds sometimes in large 
bodies, and rained down, causing astonishment, wonder, and 
superstition. 



WATER. Ill 

Water is the product of the combustion of hydrogen in oxy- 
gen, or the atmosphere, by action of lightning or electricity. 
The action of the voltaic current also decomposes water, set- 
ting free its component gases, the combustible hydrogen, 
and the supporter of combustion, oxygen. And may we 
not anticipate that in the not far distant future that water 
will be used as our combustible material. When that takes 
place, water in the form of steam will cease to be the power, 
and water itself will be the substitute. 

Acidulous Springs. — Waters that are charged with car- 
bonic acid in such quantities as to cause them to sparkle and 
effervesce when flowing from the springs are called acidu- 
lous. On account of the solvent power of this acid upon 
limestone and other rocks, such waters hold in solution lime, 
magnesia, and iron. When the latter is present, one grain or 
more to the gallon, the spring is a chalybeate. 

Almost all spring waters contain minute quantities of 
iron, generally in the form of bicarbonate. The Saratoga 
waters contain from two to three grains of this compound 
per gallon. 

Water for drinking should be boiled, then left to become 
cool and aerated. 

Distilled water must be thoroughly aerated to render it 
palatable and wholesome. 

Charcoal has the property of purifying water contami- 
nated by organic matter. When rain-water cisterns become 
foul, it is a common practice to throw in a bushel or two of 
fresh charcoal. Permanganate of potassa is also used by 
travellers, who carry with them a small vial of the crystal- 
lized salt : a small particle added to a glass of water renders 
it pure in a few moments. Impure water placed in casks on 
shipboard sometimes undergoes a kind of fermentation, by 
which the impurities are worked off and the water ren- 
dered wholesome. 



112 



WATER. 



A calculation has been made by which it appears that .°>6 
cubic miles of water are poured into the* ocean daily by the 
rivers, and it would take o0,000 years for all the water to 
rise as vapor and fall as rain, and make one trip back to 
the ocean. 

Sea-water, according to the analysis of Dr. Murray, at the 
specific gravity of 1.039, contains 

Muriate of soda, 220.01 = 

Sulphate of soda, 33.1 = 

Muriate of magnesia, 4 2. 08 = 



i 

4^ 






Muriate of lime, 



7.84 
303^09 



! 



1 



Of salt water, a cubic foot w a cubic inch, 

.3721 lbs. 



Saline Contents of Sea-Water from Different Localities. 



Baltic 


. 6.60 


Equator . 


. 3 


Black Sea 


. 21.60 


South Atlantic 


. 4 1 .20 


Arctic 


. 28.30 


Sea nf Marmora 


. 42.00 


Irish Sea . 


. 33 


North Atlantic 


12.60 


British Channel 


. 35.50 


Dead Sea 


361 


Mediterranean. 


. 39.40 







There are G2 volumes of carbonic acid in 1000 part- of 
sea-water, and all the metallic substances are held in solu- 
tion in small proportions. 



Analysis of One Gallon of Sea -Water from the Atlantic Ocean, 

made by Von Bilbra. 

Specific Gravity 1.0275 



Chloride of Sodium 1671.34 
Chloride of Magne- 
sium . . . 199.66 



Chloride of Iron . Tr 
Bromide of Sodium. 31.16 
Iodide of Sodium . Tract' 



WIXD. 



113 



Silver . 
Copper 
Lead . ■ 
Arsenic 
Silica . 
Organic matter 

Total grains in U. S. gallon . 

Percentage by weight ..... 
Water 



Sulphate of Potassa 108.46 
Sulphate of Magne- 
sia . . . 34.09 
Sulphate of Lime . 93.30 

Phosphate of Soda Trace 
Carbonate of Lime " 



Trace 



2138.91 

3.569 
96.431 



Weight of one gallon is 59.922 grains. 

Dead Sea water, percentage by weight . 
Water 



100 

19.733 
80.267 



Weight of one gallon is 68.352 grains. 



100 



The Herepaths' Analysis. 



The Atlantic Ocean 

The Dead Sea 

The Great Salt Lake 

Lake Ooroomeeyah, in Persia. 



Density. 



1.027 
1.172 
1.170 
1.188 



Grains Saline 
Matter in 

One Gallon. 



2.139 

13.488 
15.203 
18.209 



Oz. Saline 
Matter in 

One Gallon. 



4.89 
30.86 
34.72 
41.69 



Wind. 

Atmospheric air extends about 45 miles from the surface 
of the earth. Its component parts are -f- nitrogen and ^ 
oxygen, or 77, N., 23, O. It generally contains a trace of 
carbon, hydrogen, and ammonia. Greatest known heat of 
the air in the sun, 145° Fall.; greatest known cold below 
zero, 65° Fah. 

The mean pressure generally admitted is 14.7 lbs. per 
10* H 



114 



W IXD, 



square inch; barom. 30 and 34 feet water; specific gravity 
compared with water, .0012046. 

The mean weight of a column of air a foot square, and 
of the altitude of the atmosphere, is equal to 2116.8 lbs. 
avoirdupois; the rate of expansion, and also all elastic 
fluids for all temperatures, is uniform; from 32° to LM2 3 
they expand from 1000 to 1376, equal to ^ i^* of their bulk 
for every degree of heat. 

At 7 miles from the earth's surface, the air is 4 times 
rarer or lighter than at the earth's surface; at 14 miles, 
16 times ; at 21 miles, 64 times, and so continues in the 
same ratio. At a temperature of 33°, the mean velocity 
of sound is 1100 feet per second, and b increased or dimin- 
ished half a foot for each degree above or below • 

* ? l y - equals .< b degree. 





Velocity and Pressure of Wind. 


Miles 
per hour. 


Feel pex 
minute. 


Bquan 
»VOil . 


LBKS. 


1 


88 




Barely observable. 


2 
3 


170 
264 


.020 

.045 


• Perceptible. 


4 


352 




Pleasant breeze. 


5 


410 


.125 


) 


6 


528 


.180 


-.tie, pleasant wind. 


8 


701 


.320 


J 


10 
15 


880 
1320 


1.125 


I Brisk blow. 


20 
25 


1760 

2200 


2.000 
3.125 


1 Very brisk. 


30 
35 


2G40 
3080 


4.500 
6.125 


1 Iligli wind. 


40 
45 


3520 
3960 


8.000 
10.125 


> Very high. 


50 


4400 


12.500 


Storm. 


60 


5280 


18.000 


Violent storm. 


80 


7040 


32.000 


Hurricane. 


100 


8800 


50.000 


Tornado. 



TRACTION. 



115 



Traction. 

The tractive power of a horse diminishes as his speed in- 
creases. The traction of a horse on a level road, pulling 
for ten hours in the day, is as follows : 



Miles 


Lbs. 


Miles 


Lbs. 


per hour. 


Traction. 


per hour. 


Traction. 


3 
4 


. 333.33 


21 


111.11 


1 


250. 


2J 


100. 


11 


200. 


2| 


90.91 


1J 


166M 


3 


83.33 


If 


142.86 


3J 


71.43 


2 


125. 


4 


62.50 



A horse travels 400 yards, at a walk, in 4^ minutes; at a 
trot, in 2 minutes; at a gallop, 1 minute. Average weight, 
1,000 lbs. Carrying a soldier and equipments, 225 lbs., 
travels 25 miles a day of 8 hours. 

A draft horse will draw 1,600 lbs. 23 miles in one day, 
wagon included. Generally, the work allowed is equal to 
22,500 lbs., raised 1 foot in a minute, for 8 hours a day. 

A man of ordinary strength exerts a force of 30 lbs. for 
10 hours in a day, with a velocity of 2 \ feet in a second = 
4500 lbs. raised 1 foot in a minute = | the work of a horse. 

A foot soldier travels in one minute, in common time, 90 
steps = 70 yards ; in quick time, 110 steps = 86 yards; in 
double-quick time, 140 steps = 109 yards, and occupies in 
the ranks a front of 20 inches and a depth of 13, without a 
knapsack. Interval between the ranks, 13 inches; average 
weight of man, 150 lbs. Five men can stand in a space of 
1 yard square. 

A man travels without a load, on level ground, during 
8^ hours a day, at the rate of 3.7 miles per hour, or 31| 
miles per day. He can carry 111 lbs. 11 miles per day. 



116 



MISCELLANEOUS. 



Compressibility of Liquids. 

BY L. CAILLETET. 



Distilled water, free from air 
Sulphide of carbon 

Alcohol 

Petroleum oil 

Petroleum essence, benzoline 
Sulphuric ether 

Sulphuric acid i fluid | 





Temper- 


Csp.gr.). 


ature. 


1.000 


8° 




8° 




) 9° 


0.S58 


C ''° 




J 11° 




11° 








10° 




14° 



Comi 
sibility. 



0.0000 I'd 
0.0000980 
0.0000676 
0.0000701 
►0727 
0.000" 
0.000 
0.0001440 
0.0003014 



No. of 
atmos- 
pheric 

I 



706 

CUT 
174 

610 

G30 

GOG 



Compressibility. 

BY MR. CANTON. 



Spirit of Wine 
Olive Oil. 
Rain- Water 
Sea 
Mercury . 



0.00006G of its bulk. 
0.000048 " 
0.000046 " 
0.000046 " 

0.000003 " 



To Measure Round Timber. 

Multiply the length in inches by the square of ■] the 
mean girth in inches, and the product divided by 1728 will 
give the contents in cubic feet. 

When the length is given in feet and the girth in inches, 
divide by 144. 

When all the dimensions are in feet, the product is the 
contents without a divisor. 

Example. — The girth of a piece of timber 31.416 and 



MISCELLANEOUS. 



117 



62.832 inches, and its length 50 feet : required its contents. 
MlAitfULUUL + 4 = H.781, and 11.781 2 X 50 -*- 144 = 
48.1916 cubic feet. 



Capacity of Cisterns 


in U. S. Gallons for each 10 Inches in 




Depth. 


2 feet in diameter 


19.5 


8 feet in diameter 313.33 


2i 


< K 


30.6 


8i 




353.72 


3 


< it 


44.06 


9 




396.56 


3} 


i a 


59.97 


9} 




461.40 


4 


i u 


78.33 


10 




489.20 


Ah 


( u 


99.14 


11 




592.40 


5 


t a 


122.40 


12 




705. 


5J 


( a 


148.10 


13 




827.4 


6 


i «( 


176.25 


14 




959.6 


6* ' 


< « 


206.85 


15 




' 1101.6 


7 


< «( 


239.88 


20 




( 1958.4 


7i 


< «< 


275.40 


25 




' 3059.9 



Hills in an Acre of Ground. 



40 feet apart, 27 hills. 



35 


35 


30 


48 


25 


69 


20 


108 


15 


« 193 


12 


« 302 


10 


' 435 



6 


ipa.il, uou nil 
1210 " 


5 


1742 " 


3i ' 


3556 " 


3 


4840 " 


2} « 


6969 " 


2 


1 10980 " 


1 


1 43560 " 



118 



ALLOYR, 



Alloys. 



Compositions. 


z 
- 


■J 

9 


2.6 

1.1 
10. 

7. 
8. 

• • 


- 


1 1- 

1 I!. 




Chinese white copper 
( h i nese si 1 ver 


40.4 
65.2 

i 

91.4 

8. 


25. 1 
19.5 

1. 
1. 

5. 


31.6 

1:5. 

1. 


9. 

1.7 


4. 
4. 
1. 


4. 


•1. 
1. 




1J 


White argentane 

Pinchbeck 


( i( rnmii silver 


Britannia metal 

When fused, add... 
Printing metal 

Small type and ster- 1 

eotype plates. 
Telescopic mirrors.... 

Bronze Btatuary 

L;i rffe can nun 


Sni;i 1 1 cannon 


Medals 

( ymbals 

Tutenag copper 

Newton's fusible 
metal. It. melts 
at a temperature 

less than that of 
boiling water. 
A metal that ex- l 

panda in cooling. \ 



The more infusible metals Bhould 1-e melted first 



23 cubic feet of sand, or 18 cubic feet of earth, or 17 
cubic feet of clay, make a ton. 

18 cubic feet of gravel or earth before digging mak 
cubic feet when dug. 

A chaldron of bituminous coal yields about 10.000 cubic 
feet of gas, and 1.43 cubic feet of gas per hour give a light 
equal to one good candle. 3 cubic feet = 10 candles. 



MISCELLANEOUS. 



119 



10 cubic } T arcls of meadow hay weigh a ton. When the 
hay is taken out of large or old stacks, 8 and 9 yards will 
make a ton. 

Cast-iron expands l6 ^ 0ft0 of its length for one degree of 
heat; greatest change in the shade in this climate, yy-o 0I> 
its length ; exposed to the sun's rays, yw^; shrinks in cooling 
from -g 1 - to 7/y of its length ; will bear, without permanent 
alteration, 15.300 lbs. upon a square inch, and an exten- 
sion of jttVq of its length. 

Wrought iron expands Yi'iooo °f ^ s length for one degree 
of heat; will bear on a square inch, without permanent 
alteration, 17.800 lbs., and an extension in length of y^o \ 
cohesive force is diminished -§•§■$-$ by an increase of 1 degree 
of heat compared with cast-iron ; its strength is 1.12 times, 
its extensibility 0.86 times, and its stiffness 1.3 times. 



Comparative Weight of Timber in a Green and a Seasoned 

State. 



Timber. 



English Oak... 

Cedar 

Riga Fir 

American Fir 

Elm ■ 

Beech 

Ash 



Weight of Cubic Foot. 



Green. 



Lbs. Oz. 
71.10 
32. 
48.12 
44.12 
66.8 
60. 
58.3 



Seasoned. 



Lbs. Oz. 
43.8 
28.4 
25.8 
30.11 
37.5 
53.6 
50. 



The average weight of the timber materials in an English 
vessel of war is about 50 lbs. to the cubic foot, and for 
masts and yards about 40 lbs. 



120 



BOARD MEASURE TABLE. 



Table of Board Measure. 

The first left-hand column contains the breadth in inches, 
top of the columns contains the length in feet. 



The 





7 

FT. 


8 

FT. 


9 

FT. 


10 

FT. 


11 

FT. 


12 


13 

FT. 


14 

FT. 


15 

IT. 


16 

IT. 


17 

FT. 


is 

FT. 


3 


1.9 


2.0 


2.3 


2.6 


2.9 


3 


3.3 


3.6 




40 


05 




4 


2.4 


2.8 


3.0 


3.4 


3.8 


1 1.1 


4.8 




5,1 




6.0 


J5 
6 


2.11 
3.6 


3.4 


3.9 


4.2 


4.7 


.-> 5.5 


5.10 


o.:; 




7.1 


7.6 


4.0 


4.6 


5.0 


5.6 


6 


o..; 


7.o 


7.0, 






9.0 


7 


4.1 


4.8 


5.3 


5.10 


6.5 


7 


7.7 






0.1 


0.11 




8 


4.8 


5.4 


6.0 




7.4 


8 






10.0 

11.:; 


11.4 
12.0 12.0 


13.6 


10 


5.3 


6.0 


6.9 


7.6 




9 


9.9 


10.6 


5.10 


6.8 


7.6 


8.4 




10 


10.10 ll.s 


12.6 


13.4 11.2 


15.0 


11 


6.5 


7.4 




9.2 


10.1 

ll.o 


11 


11.11 12.10 


18.0 


10.(1 


15.7 
17.0 


16.6 
19.6 


12 


7.0 


8.0 


9.0 


10.0 


18.0 


14.0 


15.0 


13 
14 


7.7 




9.9 10.10 11.11 


13 


11.1 


15.2 


lo,.:; 


17.1 


8.2 


9.4 


10.6 ll.s 12.10 
11.3 12.6 13.9 
12.0 13.4 1 L8 


11 
15 

10 


15.2 


16.4 


17.o, 


18.8 


L9.U 


15 
16 


S.O 
0.1 


10.0 
10.8 


L7.6 18.9 

!7.l 


21.1 


21.3 22.0 
24.0 


17 


9.1] 


11,1 


12.9 1 L2 15.7 
13.6 15.0 16.6 
1 L3 15.10 17.5 
15.0 16.8 18.4 


17 
18 


18.5 


19.10 


21.:; 


21.1 


25.0 


18 


10.6 


12.0 


19.6 


21.0 
22.2 


23.9 


21.o 25.6 27.0 


19 11.1 


12.8 


19 
20 
21 


20.7 
22.9 


25.1 20,. 11 


28.6 


2011.8 


13.4 

l L0 


2:;. 1 


25.0 




28.4 


30.0 
31.6 


21 


12.3 


15.9 


17.6 
18.4 


10.0 


2 1.0 


26.3 






22 12.10 14.8 


16.6 


20.2 


22 


23.10 




27.6 


51.2 




23 13.5 


15.4 


17.3 19.2 


21.1 


23 


21.11 


20.10 


0)2.7 


34.6 


24 


14.0 


16.0 


18.0 20.0 


22.0 


24 


20.0 


28.0 


30.0 


32.0 34.0 


36.0 


25 


14.7 


16.8 


1S.9 20.10 22.11 


25 


27.1 


29.2 


81.8 


33.4 55.5 


37.0 


26 15.2 


17.4 


19.6 21.8 23.10 


20 


28.2 


30.4 


2,2.0 


36.10 




27 15.9 


18.0 


20.8 22.6 


24.9 


27 


29.3 


81.0) 


33.9 






28 16.4 


18.8 


21.0 


23.4 


25.8 


28 




32.8 
33.10 

85.0 


35.0 
37.6 


07.4 




42.0 


21) 16.11 


19.4 


21.9 24.2 


26.7 


29 


31.5 


11.1 




30 17.6 


20.0 


22.6 25.0 


27.(5 


30 


82.0 


40.0 42.6 15.0 



BOARD MEASURE TABLE. 



121 



Table of Board Measure — Continued. 



Q 


19 

FT. 


20 

FT. 


21 

FT. 


22 

FT. 


23 

FT. 


24 25 

FT. FT. 


26 27 28 29 30 

FT. FT. FT. FT. FT. 


3 


4.9 


5.0 


5.3 


5.6 


5.9 


6 6.3 


6.6 6.9 7.0 7.3 7.0 


4 6.4 


6.8 


7.0 


7.4 


7.8 


8 8.4 


8.8 9.0 9.4 9.8 10.0 


5 7.11 8.4 


8.9 


9.2 


9.7 


10 10.5 


10.10 11.3 11.8 12.1 12.6 


6 9.6 10.0 


10.6 11.0 


11.6 


12 12.6 


13.0 


13.6 14.0 14.6 15.0 


7 11.1 11.8 


12.3 12.10 


13.5 


14 14.7 


15.2 


15.9 16.4 16.11 17.6 


812.8 13.4 


14.0 14.8 


15.4 


16 16.8 


17.4 


18.0 18.8 19.4 20.0 


9 14.3 15.0 


15.9 16.6 


17.3 


18 18.9 


19.6 


20.3 21.0 21.9 22.6 


10 15.10 16.8 


17.6 18.4 


19.2 


20 20.10 


21.8 22.6 23.4 24.2 25.0 


11 17.5 18.4 


19.3 20.2 


21.1 


2^ 22.11 23.10 24.9 25.8 26.7 27.6 


12 19.0 


20.0 


21.0 22.0 


23.0 


24 25.n 


26.0 27.0 28.0 29.0 30.0 


13 20.7 21.8 


22.0 23.10 


24.11 


26 27.1 


28.2 2 5 32.6 


14 22.2 23.4 


24.0 25.S 26.10 


28 


29.2 


30.4 31.6 32.8 33.10j35.0 


15 23.9 25.0 


20.3 27.6 28.9 


30 


31.3 


32.6 :: 


37.6 


16 25.4 j 26.8 


28.0 29.4 


32 


33.4 


36.0 37.4 38.8 40.0 


17 26.11 28.4 


29.9 31.2 32.7 


34 


35.5 


36.10 38.3 39.8 41.1 42.6 


18 28.6 30.0 


31.6 33.0 34,6 


36 


37.6 


39.0 


40.6 42.0 43.6 45.0 


19 30.1 31.8 


33.3 34.10 36.5 


38 39.7 


41.2 


42.9 44.4 45.11 47.6 


20 31.8 33.4 


35.0 36.8 


38.4 


40 


41.8 


43.4 


45.0 46.8 48.4 


50.0 


21 33.2 35.0 


36.9 38.6 


40.3 


42 


43.9 


45.6 


47.3 49.0 50.9 52.6 


22 34.10 36.8 


3S.6 40.4 42.2 


44 45.10 


47.8 

49.10 


49.6 51.4 53.2 55.0 


23 36.5 


38.4 


40.3 42.2 


44.1 


46 


47.11 


51.9 53.8 55.7 


57.6 


24 


38.0 


40.0 


42.0 44.0 


46.0 


48 


50.0 


52.0 54.0 56.0 58.0 


60.0 


25 


39.7 


41.8 


43.9 45.10 


47.11 


50 52.1 


54.2 50.3 58.4 60.5 


62.6 


26 41.2 


43.4 


45.6 


47.8 


49.10 


52 54.2 


56.4 


58.6 60.8 62.10 65.0 


27 42.9 


45.0 


47.3 


49.6 


51.9 


54 


56.3 


58.6 


60.9 63.0 65.3 67.6 


28 44.4 


46.8 


49.0 


51.4 


53.8 


56 


58.4 


60.8 


63.0 65.4 67.8 70.0 


2945.11 


48.4 


50.9 53.2 


55.7 


58 60.5 


62.10 65.3 67.8 70.1 


72.6 


3047.6 


50.0 


52.6 55.0 


57.6 


60 62.6 


65.0 


67.6 70.0 72.6 


75.0 



Example. — To find the contents 
for the column headed 19 feet, and 
meeting of the breadth and length 

11 



of a board 19 feet long and 25 inches broad, look 
in the first column for 25 inches ; in the line of 
, you have 39 feet, 7 inches, as the contents. 



122 



TELEGRAPH ALPHABET. 






< 
I 



pq 
I 

a 



PQ 
I 



I 



7 A 



- - I _ 



g< u. - — 






M :• " 
ri (4 - d fc 



■s 



P< 

EH 

B 

o 



V 

^ : 



^s . 



\ 



^ 



*5 

1 



I 



I 



\ 



& 

^ 

S" 



<2i 



Ph 



i v 



ill 






pq 



**• 



to 
z 



- 
pq 
pq 



to 



s i 






<•■■ *j 






BB C — - B 

_ — i- -r i- 



- 



si I 

1 £S 



I. till 

: :: — 



.^ n a 



o 

I 

to 



« a 



O O M M 



to 
I 



2 fl — — 



to 
I 



C 



Ph y 



to to to c c o ~ 



M 
C* 



TABLE OF RESISTANCE MEASUREMENT. 123 



Resistance Measurement of No. 9 Galvanized Iron Wire. 



OHMS. 


MILES. 


OHMS. 


MILES. 


OHMS. 


MILES. 


OHMS. 


MILES. 


OHMS. 


miss. 


tV 


41 f 


106 6 


8 


230 


17% 


390 


29% 


675 




s 

To 


204 f 


110 


8% 


235 


17% 


400 


30 


680 


51 


1 


406 f 


115 


8% 


240 


18 


410 


30% 


700 


52% 


2 


813 f 


120 


9 


245 


18% 


41 3 3 


31 


720 


54 


3 


% 


125 


m 


250 


18% 


420 


31% 


725 


54% 


5 


% 


130 


9% 


253 3 


19 


420 6 


32 


750 


06A 


10 


6 
8 


133 3 


10 


255 




430 


32% 


760 




13 3 


1 


135 




260 


19% 


440 


33 


775 




15 


i% 


140 


WA 


205 


19% 


450 


33% 


800 


60 


20 


1% 


145 


10% 


266 6 


20 


453 3 


34 


S25 


61% 


25 


1% 


146 6 


11 


270 


2 


460 




840 


63 


266 


2 


150 ' 


11% 


275 


20% 


466 6 


35 


850 


63% 


30 


2% 


155 


11% 


280 


21 


47') 


35% 


S75 


65% 


35 


2% 


160 


12 


285 


21% 


480 


36 


880 


66 


40 


3 


165 


12 \ 


290 




490 


36% 


900 


67% 


45 


3% 


170 


12% 


293 3 


22 


493 3 


37 


920 


69 


50 


3% 


173 s 


13 


295 


222 i 


500 


37% 


925 


69% 


53* 


4 


175 


13% 


300 


22% 


506 6 


38 


950 


71% 


.55 


4% 


180 


13^ 


306 6 


23 


510 


38% 


960 


72 


60 


4% 


185 


13% 


310 


23% 


520 


39 


975 


73% 


6o 


&i 


186 6 


14 


320 


24 


530 


39% 


1,000 


75 


666 


5 


190 


14% 


330 


24% 


533 3 


40 


2,000 


150 


70 


5% 


.195 


14% 


333 3 


25 


540 




3,000 


225 


75 


5% 


200 


15 


340 


25% 


546 6 


41 


4,000 


300 


80 


6 


205 


15% 


346 6 


26 


550 


41% 


5,000 


375 


85 


6% 


210 


15% 


350 


26% 


560 


42 


6,000 


450 


90 


6 3 A 


213 3 


16 


360 


27 


575 


43% 


7,000 


525 


93 3 


7 


215 


16% 


370 


27% 


600 


45 


8,000 


600 


95 


7% 


220 


16% 


373 s 


28 


625 


46% 


9,000 


675 


100 


7% 


225 


16% 


380 


25% 


640 


48 


10,000 


750 


105 


7% 


; 226 6 


17 


3S6 6 


29 


650 


48% 


20,000 


1500 



124 



TABLES. 



Table of Number of Feet Bare Copper Wire to the Pound. 



Birming- 
ham Wire 
Gauge 


Diameter in 

Inches. 


Number of 

Bare 

Wire in Lb. 


Birming- 
ham Wire 
hge. 


Diameter \u 
Inch 


Numb 

Wire in Lb. 


1 


.300 


3.S2 


21 


.035 


280 1 


2 


£80 


4.44 


* *22 




$1.6 


3 


.260 


5.09 






-15 


4 


.240 


6.00 


*2 1 


.025 


533.1 


5 


:2-2o 


7.11 




.023 


68 


6 


.200 






.019 


2 ■;. 4 


7 


.185 


10.< 


27 


.018 


1O29.0 


8 


.170 


11.91 




.016 


2.0 


9 


.155 


1 L32 


29 


.015 


1481.4 


10 


.1 10 


L7.50 


*30 


.014 


171 = 


11 


.125 


22.1 


31 


.012 


231 


*12 


.110 






.010 


33:;. 


*13 


.095 


37.2 


33 


.00!> 


-1.4 


*14 


.085 


48,0 




.0096 


3611 


If, 


.07.-) 


61.3 


35 






*16 


.065 


81.9 


36 


.0079 


10.0 


17 


.057 


106.1 


37 


.0007 


7425.6 


*18 


.050 


137.9 


38 


.00 


18.7 


19 


.045 


161.3 


39 


.0042 


96:1 


*20 


.040 


'215.6 


40 




'J 11' 15.0 






Weight of Insulated Office Wires. 



Description. 



Kerite 

CI 

G atta-Percha 

u a 

Braided, paraffined, and compressed 

<< a it it 

a u a u 

Paraffined, single cover 

Cotton covered, plain 



Btubb's 

<.A l '.I . 



14 
16 

14 
Hi 
14 
10 
18 
19 
16 
18 
19 
20 



ii it peb Lb, 



50 

:^ 
65 

48 

75 
175 

115 

215 



M T S C E L T, AXEO U S . 



125 



Table of Iron Wire. 



Birming- 
ham Wire 
Gauge. 


Diameter 
in Inches. 


Weight 

100 feet. 


Weight 
One Mile, 

Galvan- 
ized. 


One Mile, 
not Gal- 
vanized. 


Breaking 

Strains. 


Length of 
Bundles 
in Feet. 


o ... 


0.340 


29.44 


1490 


1416 


7280 


213 


1 ... 


0.300 


22.92 


1210 


1150 


5650 


273 


2 ... 


0.280 


19.97 


1054 


1002 


4930 


315 


3 ... 


0.260 


17.22 


909 


854 


4250 


"363 


4 ... 


0.240 


11.00 


7/ 5 


747 


3620 


429 


5 ... 


•0.220 


12.34 


651 


619 


3040 


510 


6 ... 


0.200 


10.19 


538 


512 


2510 


609 


7 ... 


0.185 


8.72 


461 


438 


2220 


717 


8*... 


0.170 


7.37 


389 


370 


1840 


858 


9* ... 


0.155 


6.12 


323 


307 


• 1560 


1026 


10*... 


0.140 


4.99 


264 


251 


1280 


1260 


11*... 


0.125 


3.98 


211 


200 


1000 


1587 


12*... 


0.110 


3.08 


163 


157 


800 


2100 


13 ... 


0.095 


2.35 


124 


118 


568 


2679 


14 ... 


0.085 


1.84 


97 


93 


456 


3426 


15 ... 


0.075 


1.43 


76 


73 


352 


4404 


16 ... 


0.065 


1.08 


57 


55 


264 


5862 


17 ... 


0.057 


0.83 


44 


42 


208 


7620 


18 ... 


0.050 


0.64 


34 


32 


160 


■ 9450 


19 ... 


0.045 


0.52 


27 


26 


128 


12255 


20 ... 


0.040 


0.41 


21 


20 


104 


14736 



* Those marked with a star are standard sizes for telegraph use. 



The Mail Steamer Baltic ran from Liverpool to New 
York, in 1853, in 9 days, 16 hours, and 33 minutes; and 
from New York to Aspinwall, in 1859, in 6 days and 16 
hours, and returned in 6 days and 22 hours : — distance, 
1980 miles each way. 

The Mail Steamer Adriatic ran- from New York to 
Liverpool, in 1860,'ih 9 days, 13 hours, and 30 minutes; 
from Galway to Quarantine, New York, in 8 days, 12 hours, 
and 30 minutes, touching at St. John's, N. B. On a passage 
from New York to Liverpool she ran 365 knots in 24 hours, 
and in 1861 she ran a measured mile in England in 3 min- 
utes and 18 seconds = 18.181 knots per hour. 
11* 






126 MISCELLANEOUS. 

The Mail Steamer Vanderbilt, of New York, ran from 
New York to the Needles, in 1857, in 9 days and 8 hours ; 
and from the Needles to New York, in 1859, in 9 days, 9 
hours, and 26 minutes. 

British and North American Royal Mail Steamship Com- 
pany's Steamer Persia, of Glasgow, ran from New York to 
Liverpool, in 1856, in 9 days, 1 hour, and 45 minutes; and 
from Liverpool to New York, in 1861, in 9 days, 18 hours, 
and 1 minute. 

Steamer Ocean Bird, of New York, ran from New York 
to Havana in 4 days and 4 hours. 

Steamship Daniel Drew, of New York, ran from Jay 
Street, New York, to Albany, in 7 hours and 20 mi- 
tide favorable, but wind ahead. Her time to Hudson, 126 
miles, deducting landings, was 5 hours and 5 minutt I 

through the water fully 22.3 miles per hour. 

Sovereign of the Seas, (clipper ship,) of Boston, in 22 days 
sailed 5391 knots, or 2-15 knots per day. For 4 day- >he 
sailed 341.78 knots per day, and for 1 day 375 knots. 

Northern Light, (clipper ship, I of Boston, sailed from San 

Franeisco to Boston in 70 days and 8 hours. 

Fiijhig Cloud, (clipper ship,) of Boston, sailed 374 knots 
in 1 day. 

Red Jacket, (clipper ship,) of New York, sailed from N< w 
York to Liverpool in 13 days, 1 hour, and 25 minutes. 

Nightingale, (clipper ship,) of New York, sailed from New 
York to Melbourne in 73 days. 






DECIMAL TABLE. 



127 



Decimal Table 

Fok Reducing Vulgar to Decimal Fractions. — In a 
line with the numerator and under the denominator is the 
equivalent decimal fraction ; thus, T 9 2 = 0.75 ; t 6 q- = 0.375. 
8ths and 4th s may be had from 16ths ; 6ths and 3ds may be 
had from 12ths. 



Numerator. 


Denominator. 


Denominator. 


Denominator. 




12ths. 


16ths. 


96ths. 


1 


0.08333 


0.0625 


0.0104166 


2 


0.1C666 


0.1250 


0.0208333 


3 


0.25000 


0.1875 


0.0312500 


4 


0.33333 


0.2500 


0.0416666 


5 


0.41666 


0.3125 


0.0520833 


6 


0.50000 


0.3750 


0.0625000 


7 


0.58333 


0.4375 


0.0729166 


8 


0M666 


0.5O00 


0.0833333 


9 


0.75000 


0.5625 


Eighths of an 


10 


0.83333 


0.6250 


inch reduced 


11 


0.91666 


0.6S75 


to the deci- 


12 


1.00000 


0.7500 


mal of a foot. 


13 
14 




0.8125 
0.8750 






15 




0.9375 







Reduce 6 feet 4^ inches to -the decimal of a foot by the 
above. 

6.00000 = 6 feet. 
.33333 = 4 inches. 
.04167 = 4 8ths. 



Feet, 6.37500 



Heat-Radiating Power of Different Bodies. 



Water 100 

Lamp-black 100 

Writing-paper. ... 100 

Glass 90 

India-ink 88 



Bright lead 19 

Silver 12 

Blackened tin 100 

Clean tin 12 

Scraped tin 16 



Ice 85 

Mercury 20 

Polished iron 15 

Copper 12 






128 



TABLE. 



Table for Finding the Distance of Objects at Sea in 
Statute Miles. 



Height 


Distance 


Height 


Distance 


Height 


Distance 


Height 


Distance 


IN 


IN 


IN 


EM 


IN 


IN 


IN 


IN 


Feet. 


Miles. 


Feet. 


Mn 


Feet. 


Miles 


Feet. 


Miles. 


*.582 


1. 


11 


4.39 


30 


7. 2 7) 


200 




1 


1.31 


12 


4.58 




7.-:; 




22.91 


2 


1.87 


13 


4.77 


40 




400 


26.46 


3 


2.29 


14 


L95 


45 


-.-7 


.71.0 




4 


2.63 


15 


5.12 


50 




1000 


32.41 


5 


2.96 


16 


5.29 


60 


10.25 




59.20 


6 


3.24 


17 


5.45 


70 


11.07 




72.50 


7 


3.49 


18 


5.61 


80 


11.83 


4000 




8 


3.73 


19 


:..77 


90 


1 2.55 




93.5 


9 


3.9G 


20 


5.92 


loo 




I mile. 




10 


4.18 


25 


6.61 


150 


16.20 







(.99 inches. 

The difference in two levels is as the square of the distance. 
Thus, if the height is required for 2 miles : 
1 2 :2^::G.!)!):27.!)(5 inch 
For geographical miles, the distance i'or one mil. 
inches, 

Example. — If a man al the fore-top-gallant masthead of 
a ship, 100 feet from the water, sets another and a large ship 
(hull to), how far are the ships apart? 

A large ship's bulwarks are, Bay 20 fret from the water. 
Then, by table, 100 feet = 13.23 
20 " = 5.92 

Distance, 19.15 miles. 
Note. — -fa should be added for horizontal refraction. 



Heat-Conducting Power of Different Bodies. 



Gold 1000 

Silver 973 

Iron 374 

Tin 304 



Marble 'J 1 

Fire-brick 11 

Platinum 381 

Copper SOS 



Zinc 

Lead L80 

Porcelain 12.2 

Fire-clay 11.4 



PRODUCTS OBTAINED FROM COAL. 



129 



Products Obtained from Coal. 

BY HENRY A. MOTT, JR. 



Hi 

o 
O 



Gas,illu-1 



• J 



minatinj 

etc. 

Tar 

Ammonia? 

Water. ) 

Coke, for ? 

Fuel. 3 



r Oils, 
30 % 



ii 



r-n t ( Benzole MOed to make 
|Benzole lToluol \\ An[Vm ^ 



Naphtha J Naphtha \ p Used for Varnishes. 
[Xylole . . . Used for Small-pox. 

FURNISHES 

f Carbolic Acid? (Used for Disin- 
Cresylic Acid) \ fectants. 
^Dead Oil -J Naphthaline . . . Dyes, etc. 

Anthracene \% ? (Used to make 
3 I A 



X'hrvsene 



Alizarine. 



Pitch? (Used for Roofing and Pavements. 
70 fo ) (Anthracene, 2 per cent. 



The preparation of Alizarine from Anthracene : 

Potassic 
Anthracene. Acetic Acid. Bichromate. Anthraquinone. 

C^ 4 H 10 + Cfl&t . + K 2 Cr A = C 14 H0. 2 + etc. 
Anthraquinone. Bromine. Dibromoanthraquinone. 



C U H 8 2 + 2 Br = C 14 II 6 Br 2 2 + etc. 

Dibromoanthraquinone. Potassic hydrate. Alizarine. 



Ci 4 H 6 Bi\ 2 2 



+ 



9 HKO 



= Cu&fPt +etc. 



Products Obtained by the Distillation of Coal. 


NAME. 


FORMULA. 


GAS OR VAPOR. 

SPEC. GRAVITY. 


BOILING-POINT. 
DEGREES. 


Atmospheric air 




1.000 

0.069 

0.971 

1.106 

0.590 

0.622 

0.967 

1.529 

1.801 

2.2112 

2.645 

0.5596 

1.037 

1.522 


33 

100 

109 (Fall.) 

+ 13.09 (Fah.) 
47 


TJydro (y en 


H 

N 

O 
NH 3 
H.,0 

CO 

co 2 

CN 

so 2 

cs 2 

CH 4 
C 2 H 6 
C 3 H 8 


Nitrogen 


Oxvo'en 


Ammonia 


Aqueous vapor 


Carbonic oxide 


Carbonic anhydride 

Cyanogen 


Sulphurous anhydride... 
Carbon disnlphide 


Marsh Gas Series. 
Methvl hvdride .* 


Ethyl hydride 


Propvl hvdride 





130 



DISTILLATION OF COAL. 



Butyl hydride 

Amy I hydride 

Hexyl hydride 

Octyl hydride 

Decyl hydride 

Oleftani Gas Series, 

Methylene 

Ethylene (defiant ,L r ;; — . 
Propylene (trityjene)... 

Butylene 

Amylene 

Caproylene ( hexylene |. 

CEnanthylene 

Aeids, 

Flydrosulphocvanic 

Hydrosul phone 

( Carbolic ( phenol | 

Rosolic 

Hydrocyanic 

Acetic 

Alcohols. 

Cresylic alcohol 

Phlorylic alcohol. 

"Benzole Series, 

Benzole 

Toluole 

Xylole 

Cumole 

Cymole 

Naphthalene 

Anthracene 

Chrysene 

Pyrene 

Aniline 

Pyridine 

Picoline 

Lutidine 

Collidine 

Parvoline 

Coridine 

Rubidine 

Viridine 

Licoline 

Lepidine 

Cryptidine 

Pvrrol 



FORMULA. 



•-.it, 

C t H, 



< ir, 

H. 

I -II,,, 
Hi, 
H M 

II I 
lis 

II' 

< i : 
CgH 

II,; 

li- 
en „. 

Bu 
QA 

Hid 

II, 

II N 

i; N 

i. X 
r.ll 
(C,H M )N 

'(,,,11 
,C n I! 
M-,,II., N 

(C„H, X 

" ,,H„ N 

iC'.II 



VAPOR. 
SPEC. GRAVITY. 






0.484 

2.419 
2.97 



1.17 

-olid, 

(t.7> 



3.179 
3.179 
4.147 

4.423 
6.741 



Sp.Gr.H4O 1 
1.020 



.09613 
.921 



1.017 



BOILINO-rOI>"T. 



9 
30 

158 

39 

— 17.S 

188 



111 
129 
1 18 
175 
212 
it 218 



182 
115 
134 
154 

170 

1211 
251 

260 



SIGN OF DEATH — IRON. 131 

Sign of Death. 

The best mode of determining the death of a person is 
that by Dr. Hugo Magnus, of Breslau. It is simple, 
conclusive, and easily applied by all. When life ceases 
and the person is dead, the circulation of the blood posi- 
tively stops, and is at the end of its action. No matter how 
inactive the coma or trance, no matter how death-like the 
lethargy, some circulation will continue, be it ever so slug- 
gish. When it stops once, resuscitation is impossible. 

All that is required, therefore, is to tie a string firmly 
around the finger of the supposed corpse. If there is the 
least spark of life left, or the blood circulates at all, the 
whole finger, from the string to the tip, will gradually turn 
a bluish red, from the enlargement of the veins. Nothing 
else can be mistaken for this appearance. 



Iron. 

Iron is produced not only by chemical action in the earth, 
but also by condensation, etc., in space beyond the influence 
of our planet. It falls to the earth in the form of meteoric 
bodies, improperly called meteoric stones: the iron in this 
form is combined with nickel and other substances. All 
parts of the world have furnished specimens of these mete- 
oric irons. Some fine specimens are deposited in the Smith- 
sonian Institute, at Washington, similar in form to rings and 
bombs, and may well be termed Jove's discarded toys, sent 
to us in remembrance. 

Iron is also contained in the human blood: 100 parts of 
fibrin contain 2.151 of mineral matter and 0.0466 metallic 
iron ; 100 parts of the blood-globules contain 1.325 mineral 
matter and 0.350 iron ; 100 parts of albumen contain 8.715 
mineral matter and 0.0863 iron. 100 parts of human blood 



132 IRON. 

contain 0.3 fibrin, 7.0 albumen, 12.7 globules, 1.0 mineral 
matter, and 79.0 water. 

The first process in the manufacture of iron is melting the 
ore in the blast-furnace; here the ore, with coal and a flux 
of limestone, is piled in and kept burning day and night 
The iron, as it becomes melted, flows to the bottom of the 
furnace, and is drawn off, in a glowing stream, into moulds 
formed in the sand, which are called pins, from a fancied 
resemblance. Prior to the year 1835, wood and charcoal 
were entirely used in this country, and in that year Frederick 
W. Geisenhainer, of Schuylkill County, succeeded in pro- 
ducing iron with the hot blast and anthracite coal. 

In England, wood and charcoal were entirely used until 
1612, when Simon Sturtevant patented the smelting of iron 
by the consumption of bituminous coal, and it did not come 
into general use until many years after. 

In 1829, Neilson took out a patent in England for the use 
of the hot blast, and was by this process able to make tlr 
times the quantity at. less expense. In one Bingle case of 
infringement of his patent he received a check for damages 
for three-quarters of a million dollars. 

For converting the pig- or cast-iron into wrougtt, it un- 
dergoes the process of" boiling" or puddling, which pro* 
was invented by Henry Cort, and patented by him in El 
land, in 178'). For this invention, Cort has been called "the 
father of the iron trade'' — his invention having increased 
the wealth of England three thousand millions of dollars. 
In consequence of having expended all that he | 1 in 

experimenting for the grandeur of his country, he died a 
poor man. The iron being melted in the furnace, the pud- 
dler inserts an iron bar through a small opening and sti 
the metal until he forms it into a ball. It is then taken out 
and conveyed to the rotary squeezer. The ball of white- 
hot iron is placed in the squeezer, and forced with a rotary 






IRON. 133 

motion through a spiral passage, the diameter of which is 
constantly diminishing, which forces out all slag and cinder, 
and the ball assumes the shape of a short, thick cylinder, 
called a "bloom." This is again heated in an oven, and con- 
veyed from that to the steam-hammer, where it is pounded 
into shape and form, or conveyed to the rollers, and by 
means of them rolled into the various forms, either sheet, 
round, square, or beams and girders. 

The ninth census gives the following information relative 
to the iron industries of the United States for the year end- 
ing June, 1870. 

Pig-iron, 386 establishments ; 574 blast-furnaces (with a 
daily capacity of 8,357 tons melted metal), employing 27,554 
hands, producing 2,052,821 tons of pig, of the value of 
$69,640,498. 

Foundries, 2,653, employing 51,297 hands, and producing 
to the value of $99,837,218. 

Bloomary forges, 82, employing 2,902 hands, and pro- 
ducing 110,808 tons of blooms, of the value of 82,765,623. 

Forges, 103, employing 3,561 hands, and producing to the 
value of $8,147,669. 

Establishments producing bar, rod, and railroad iron, nail 
plates, etc., 309, employing 44,643 hands, and producing to 
the value of $120,301,158. 

Manufacture of Russia Iron. 
The iron for this purpose is refined from pig obtained 
from magnetic ore, or red and brown haematites, by the use 
of wood and charcoal. 

The conversion of pig- into wrought-iron is effected either 
in the refining fire or the puddling-furnace. The iron must 
be more granular than fibrous, and must contain sufficient 
carbon. 
12 



134 PUDDLING-FURXACES FOR IRON. 

The manufacture of iron was carried on in India long 
before its introduction into Europe, as well as the cutting 
and polishing of granite. According to a statement by 
Kichard Mallet, the production in India was carried on to 
such an extent as to rival the production of the Ian 
steam-hammer forges in Europe at the present day. 

As an illustration-, he mentions that of a wrought-iron 
pillar or column at the principal gate of the ancient mosque 
of the Kutub, near Delhi, which is as large as the screw-shaft 
of a first-class steamer, being >ixtv l\'<>t in length, and sur- 
mounted with a capital of elaborate Indian design, carved 
by chisel in the solid iron. It contains eighty cubic !• i I of 
metal, weighs upward of seventeen tons, and contains an 
inscription dating hack fifteen centuri 



Puddling -Furnaces for Iron. 

There have been quite a number of improvements made 

in the construction of the furnaces, some of which are 
follows : 

Wood and Jackson invented an oscillating or rotary 
puddling-furnace of cylindrical form, having two skins, 
between which is a water-space for protecting the Bides of 
the cylinder from heat, and on its inner upper Burface a 
lining of brick, to reduce the amount of space, and BO prevent 
the loss of heat. At each end is a trunnion on winch the 
cylinder turns, and through which the flame from the funis 
makes its entrance and exit. These trunnions are also pro- 
tected by water-chambers. On the top and through the 
brick lining is an opening, through which the iron is fed to 
be heated, and through which it is removed when balled, the 
cylinder being partially rotated for this purpose. Beneath 
the water-space is located an air-chamber, from which a set 



IRON. 135 

of tuyeres open into the cylinder, and through them a steady 
blast is forced through the molten iron, which, combined with 
an oscillating rrfotion of the cylinder, it is said, produces a 
superior quality of iron. 

William Sellers has constructed a puddling-furnace com- 
bined with a heat-restoring apparatus, consisting of a series 
of tubes through which the waste heat passes, arranged in a 
similar manner to those in the furnace of Gorman and Paton, 
but differing in being divided into two sets — one of which 
heats gas, and the other air — so arranged that the gas and 
air, after being heated, meet in opposing columns so as to be 
thoroughly mixed before combustion, at the mouth of the 
rotary furnace, where the mixture becomes ignited, and pass- 
ing through the furnace, acts on the metal therein, and then 
enters the regenerating tubes, leaving there the most of the 
waste heat to be again taken up by the incoming air and gas. 
To remedy a difficulty experienced in starting this class of 
furnace, owing to the cold air contained in the passages, a 
flue is provided in which fire may be introduced to heat the 
air, and so induce a current. 

Improved Cupola Furnace. 

Smelting iron in a cupola furnace appears to most people, 
who see it daily done at every foundry, the simplest thing in 
the world; it is, however, not so, if due regard is taken to 
economy and good quality in casting. In a common cylin- 
drical cupola, three essential parts may be distinguished. 
The upper half or body of the furnace prepares the pig-iron 
and lime, which, together with coke, are thrown in at the top 
for smelting in the middle part or crucible, which is some- 
what narrower, and provided with numerous nozzles for the 
introduction of blast, whence the molten iron, together with 
slag, runs down to the lower part, or hearth, where it collects 
until it is tapped. 



136 IRON. 

When such a furnace is to be started, it is filled to about 
two-thirds with coke, and one-third with coke and iron ; fire 
is then introduced and the blast turned on, "when the molten 
iron collects in the hearth, and replaces the coke of the same. 
Here it necessarily takes up impurities from the coke, and 
impregnates the latter so much that it cannot be destroyed 
by the blast, and when the iron is tapped, masses of coke 
and half-melted iron, which are not any longer supported, 
tumble down in the hearth, where they are imperfectly burnt 
or melted, and cause the iron which collects there to become 
cold and sticky. These irregularities take place after every 
tap, and it generally happens that iron which was at first 
fluid and gray, suddenly becomes thick and white, and 
unsuitable for the castings intended. In order to avoid this, 
Henry Krigar, of Berlin, constructs his cupola so that the 
lower part, or hearth, is not below the crucible, but by itfi 
side, and connected with it by a slanting canal, which is 
about 3 inches high, 6 to 8 inches long, and as wide as the 
cupola. This arrangement prevents any coke or half-mel 
iron from falling down in the hearth, which is only accessible 
to melted iron and slag, and forms for them a kind of sump 
or receiver, which in no way interferes with the regular 
working of the two upper parts of the cupola. This very 
simple construction has proved highly ill, and its 

great advantages are a saving of fuel, a uniformly hot and 
liquid iron, and an increased yield per diem, as the regular 
smelting operation is never interrupted. 1 cupola 

can, therefore, be recommended not only for foundries, but 
also for Bessemer works. 

Henderson's processes consist in the use of fluorine, in con- 
junction with oxygen, which, acting on the molten cast-iron, 
in a few minutes almost completely purifies it. They are ap- 
plied to wrought-iron as follows : Fluorspar and oxides of 
iron are ground to a fine powder, mixed thoroughly, and 






IRON. 137 

thrown into the ordinary puddling-furnace. The molten 
cast-iron to be acted on is then poured over the spar and 
oxides, which remain on the bottom of the furnace; the 
furnace-door is closed, and the iron allowed to boil for about 
half an hour ; the rabble is then worked for about ten 
minutes, and the metal is balled up in the usual way. The 
whole time occupied by one charge, with ordinary gray- 
forge pig-iron, being about one hour. The mode in which 
the purification of the iron is effected appears to be as follows: 
After the cast-iron has been poured in and the furnace closed, 
the heat of the metal melts the fluorspar and oxides, which, 
combining with the silicon, sulphur, and phosphorus, and 
part of the carbon, removes them from the cast-iron in the 
form of vapor and slag, and this so effectually that, by the 
time ordinary gray-iron has had the amount of carbon in it 
reduced to 1\ per. cent., common brands of pig-iron are ren- 
dered as free from impurity as good Bessemer steel. 

The removal of impurities by the Henderson processes 
enables iron of a very high quality to be made from cinder- 
pig and other common brands of cast-iron. Although the 
tensile strength of the iron is very great, it is chiefly remark- 
able for its toughness, as will be seen from the high elonga- 
tion. Great elongation is one of the most valuable and 
peculiar properties of the iron made by the Henderson proc- 
esses. For instance, plates made in England, at Bowling Iron 
Works, Bradford, from Yorkshire cinder-pig iron, gave more 
than double the elongation of Lowmoor, Bowling andFarnley. 

The tests were made by Mr. Kirkaldy, and the following 
is a summary of them : 

Ultimate tensile Contraction of Elongation, 
strength, tons, area, per cent, per cent. 
Henderson's cinder boiler-plate, \ 9 , ^ „ 9 . 

Mean of length and crossway. j 
Bowling Lowmoor andFarnley,) 
Mean ol length and crossway. J 

1.13 15.8 12.43 

12 * 






138 IRON, 



Difference in favor of Henderson's cinder-iron, 

tensile strength 

Difference in favor of Henderson's cinder-iron, 



r 4.7S per cent. 

avor of Henderson's cinder-iron. ) 
r > 100 per cent, 

contraction of area. j 

Difference in favor of Henderson's cinder-iron. ) ,-- 

. . Y 110 per cent, 

elongation j 

Steel manufactured from wrought-iron made by these 
processes from common Scotch pig-iron gave a tan 
Btrengtb equal to steel made from the best Swedish iron; 
when made into tools:, it also stood wear equally well, 

Ira Hersey, in his process for converting iron into steel, 
has constructed a furnace in which the halls from a bloom- 
ary are transferred to an inclined hearth-floor in which the 
proper chemicals for carburizing — manganese, prussiate of 
potash, charcoal, and salt — are introduced in thin sheet-iron 
cans. The metal as fas! as melted combines with the 
chemicals and runs into a receiving basin at the bottom, 
from whence the Bteel BO formed may be drawn to form 
ingots. 

Barron's process for converting cast-iron tools into Bteel. 
Tools which are to be prepared by this pi are first 

made of cast-iron, after which they are introduced into a 
revolving drum, and all roughness worn off by attrition. 
The smooth irons are then {Kicked in layers in iron boi 
where they are closely imbedded in (day, and subjected to 
the action of oxide of iron and certain chemicals, by which 
the iron is decarburized. In th - the iron t< 

subjected to an annealing heat, which is maintained from 
three to six days. They are subsequently placed in a retort 
capable of containing about a ton of the tools, into which 
the vapor of gasolene and other carbonaceous materials are 
passed. In a few minutes the iron is converted or trans- 
formed into steel, when they are ready to be tempered, and 
ground and polished for the market. 



ANCIENT GRANITE WORKS. 139 

A. H. Siegfried's process for tempering steel by heating it 
to a cherry-red in a fire purified by throwing in salt, then 
covering the steel with the same substance, and, while sub- 
jecting it- to this treatment, working it nearly to the finished 
form. A compound of the following ingredients is then 
substituted- for the salt: one part each of salt, sulphate of 
copper, sal ammonia, and sal soda, and a half part of nitrate 
of potash ; and the steel is alternately heated and treated 
with this until it is refined and brought to the finished form. 
It is then slowly heated to a cherry-red, and plunged into a 
bath of the following ingredients : alum, sal soda, and sul- 
phate of copper, of each one and a half ounces ; nitrate of 
potassa, one ounce, and salt, six ounces, dissolved in a gal- 
lon of rain-water. 



Ancient Granite Works in the East Indian Empire. 

The art of cutting or carving in granite has never been 
equalled or carried to as great perfection as on the conti- 
nent of India. At Chillambaram, in the Carnatic, and on 
the Coromandel coast, is a congeries of temples representing 
the sacred Mount of Meru. Here are seven lofty walls, one 
within the other, round the central quadrangle, and as many 
pyramidal gateways in the midst of each side, which form 
the limbs of a vast cross, consisting altogether of twenty- 
eight pyramids. There are, consequently, fourteen in a line, 
which extend a mile in one direction. From the nave of one 
of the, principal structures there hang, on the tops of four 
buttresses, festoons of chains, in length about 548 feet; each 
garland, consisting of twenty links, is made of one piece of 
granite 60 feet long ; the links themselves are monstrous 
rings, 32 inches in circumference, and polished as smooth as 
glass. Compared with the cave temples of the southern Car- 



140 ANCIENT GRANITE WORKS. 

natic, and the monolith temples of granite at Mahabali- 
pooram, those in Egypt sink into insignificance. 

. The stone of which the cave temple of Elephants is com- 
posed resembles porphyry, and the elaborate tracery and 
sculptures with which the columns at the entrance, and also 
of the interior, are decorated, are exquisitely delicate; but 
ignorance, superstition, and blind fanaticism have committed 
strange and barbarous havoc. The area occupied by this 
temple is nearly 130 feet dee}) and about 133 broad, divided 
into nine aisles formed of twenty-six pillars, of which eight 
are broken away altogether, and most of the remainder are 
much injured. 

KEYLAS. — This cave is excavated from the solid rock, and 
is the most elaborately designed and artistically enriched of 

the caves of Ellora. The height of the outer gateway of 

Key las is fourteen feet, opening toa p with apartments 

on either side. Over the doorway is the Xogara Kliana, or 
music gallery, the floor of which forms the roofofa pa- 
leading from the entrance 1<> the excavated area within. 

Entering upon the latter, which is a wide expanse of level 

ground, formed by cutting down through the solid rock of 

the hill, an immense temple of a complex pyramidal form 

presents itself, connected with the gateway by a bridge, con- 
structed by leaving a portion of the rock during the pi 
of the excavations. 

In front of the structure, and between the gateway and 
the temple, are the obelisks of Key las, placed one on each 
side a pagoda or shrine, dedicated to the sacred bull Nun- 
dee. These obelisks are of a quadrangular form, eleven 
feet square, sculptured in a great variety of devices, all of 
which are elaborately finished ; their height is about forty- 
one feet, and they are surmounted by the remains of some 
animal, supposed to have been a lion, which, though not 
an object of Brahmanic veneration, occurs very frequently 



ANCIENT GRANITE WORKS. 141 

among the decorations of the cave temples. Approaching 
the entrance to the temple is a colossal figure of Bhawani, 
supported by a lotus, having on each side an elephant, whose 
trunks form a canopy over the head of the goddess. 

On each side of the passage, from the inner entrance, are 
recesses of great depth and proportions, in one of which, 
resting upon a solid square mass, is the bull Xundee, su- 
perbly decorated with ornaments and rich tracery. Beyond 
this, on the opposite side, is a similar recess, in which is a 
sitting figure representing Boodh, surrounded by attendants, 
and near the end of the passage, where the body of the great 
temple commences, is a sitting figure of Guttordhirj (one of 
the incarnations of Siva), with his ten hands variously oc- 
cupied. Turning to the right, the walls of the structure are 
covered by sculptures representing the battles of Bam and 
Rouon, in which the achievements of the monkey-god, Hu- 
uiayun, are conspicuously displayed. Pursuing the story de- 
picted by these sculptures to the end, the extremity discloses 
the entrances into three temples. Beturning to the en- 
trance on the left, the history of the war of the gods is con- 
tinued in sculpture. The w T hole length of the substructure 
appears to be supported on the backs of animals, such as 
elephants, lions, horses, etc., which project from the base of 
the piers in the surrounding walls, and give the superin- 
cumbent mass an air of lightness and movability. 

This extraordinary structure is in every portion of the 
exterior, as well as the interior, carved into columns, pilas- 
ters, friezes, and pediments embellished with the represen- 
tation of men and animals, singly or in groups. The gal- 
leries contain sculptured history, and forty-two gigantic 
figures of gods and goddesses. A portion of the chambers 
is richly and lavishly embellished, one containing groups of 
female figures so exquisitely proportioned and sculptured, 
that even Grecian art has scarcely surpassed the beauty of 



142 "ANCIEXT GRANITE WORKS. 

the workmanship. Pen and, pencil can afford very ineffi 
ual aid in a field so vast and unparalleled as that of the 
Keylas of Ellora. 

Their sacred character lias been lost in the obscurity of 
unknown ages, and the projectors must have d intel- 

lectual and imaginative gifts of extraordinary power. The 
rock from which this temple is wrought is a hard, red gran- 
ite, and from every peak and pinnacle of the .-acred mountain 
the eye roams over scenes of romantic .beauty and marvel- 
lous grandeur. 

According to the Brahminical account of the origin of 
these excavations, 7,^' I years have elapsed since they w 
commenced, as a work of pious gratitude, by Eeloo Rajah, 
son of Peshpout of Ellichpore, when 3,000 years of the 
Dwarpa Yoag were unaccomplished, which, added to the 
4,894 years of the present, or "Kal Yoag/ 1 completes the 
full number, 7,< V !M. 

The interior of the cave temple of Elephants is covered 
with sculpture from the entrance 4 to the fartli the 

excavation, and mystic forms meet the eye in every direction. 
A colossal triple-headed bust occupies a vast recess at the 

extremity of the central aisle of the temple. The dimensions 
of this relic are, from the bottom of the bust of the central 
figure to the top of the cap on its head, eighteen feet; the 
principal face is live feet in length, and the width, from the 
front of the ear'to the middle of the nose, is tin' four 

inches. The width of the whole bust is twenty feet. A cap 
surmounts the head of the central figure, once richly d< 
rated with superb jewels. Around the neck of the same 
figure was formerly suspended a broad collar, composed of 
precious stones and pearls, long since appropriated to a more 
useful purpose than the decoration of a block of carved stone 
in the bow T els of a mountain. 

The whole of this singular triad is hewn out of the solid 



ANCIENT GRANITE WORKS. 143 

rock, which is a coarse-grained, dark-gray basaltic forma- 
tion, called trachyete, and it occupies a recess cut in the 
rock to the depth of thirteen feet. On each side of the 
niche is sculptured a gigantic human figure, having in one 
hand an attribute of the Deity, and with the other resting 
upon a dwarf-like figure standing by its side. Niches, or 
recesses of large dimensions,, and crowded with sculpture, 
appear on either side. 

In that on the right-hand side is a colossal figure, appar- 
ently a female, but with one breast only. This figure has 
four arms : the foremost right hand rests on the head of a 
bull; the other grasps a cobra-de-capello; a circular shield is 
borne on the inner left hand. On the right of this female 
is a male figure, bearing a pronged instrument represent- 
ing a. trident ; on the left, a female bears a sceptre. Xear 
the principal figure is an elephant surmounted by a beau- 
tiful youth, and above the latter is a figure with four heads 
supported by birds. Opposite to these is a male figure 
with four arms, sitting on the shoulders of one in an erect 
posture, who has a sceptre in one of the hands ; and at the 
upper part of the back of the recess are numerous small 
sculptured figures, in various attitudes and dress, supported 
by clouds. 

Turning to the niche on the left is a statue of a male, 
seventeen feet in height, having four arms ; to the left of this 
a female fifteen feet in* height. The countenance of this statue 
is sweetly feminine, and expressive of gentleness and amia- 
bility. The head-gear of the small figure bears a resem- 
blance to the wigs worn by modern judges. 

Various conjectures have been hazarded by the learned 
as to the origin and purposes of these extraordinary cavern 
temples. The following explanation of some of the sculptures 
is from a paper preserved among the collection of the Asiatic 
Society of Bengal. 



144 



ANCIENT GRANITE WORKS. 



The triple-headed colossal bust described in this docu- 
ment is the personification of the great attributes of that 
being for whom the ancients, as well as the Hindoos of the 
present day, have entertained the most profound veneration. 
The middle head represents Brahma, or the creative power; 
that on the left, the same deity as Vishnu, or the preserver; 
that on the right, Siva, or the destructive power. The bull 
couchant at the feet of one of the deities symbolizes an at- 
tribute of Siva, under his name of Iswara. The beautiful 
youth on the elephant represents Cama, the Hindoo god of 
love. 

The terrific figure witli eight arms represents the destr 
Siva in action. The distant scene with small figures, expi 
sive of pain and distress, denotes the Bufferings of tli 
sentenced by Brahma to the place of torment ; and it is 
considered that the whole was dedicated to the worship of 
the god Siva, and to the mysteries of his cruel and impure 
ritual. 



Tin: end. 






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